Document:

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                                                                    EXHIBIT 10.1

                         REGISTRATION RIGHTS AGREEMENT

     This Registration Rights Agreement is dated as of December 13, 1999 by
and between Titan Resources Holdings, Inc., a Delaware corporation (together
with its successors and assigns, the "Company"), and Union Oil Company of
California, a California corporation ("Union Oil").

     1.   Background. The Company has agreed to issue to Union Oil certain
          ----------
shares of the Company's common stock, par value $.01 per share (the "Common
Stock"), pursuant to the transactions contemplated by (i) the Agreement and Plan
of Merger dated as of the date hereof among Union Oil, the Company, TRH, Inc.,
and Titan Exploration Inc., a Delaware corporation (as it may be amended, the
"Merger Agreement") and (ii) the Non-Dilution Agreement dated as of the date
hereof between the Company and Union Oil (as it may be amended, the "Non-
Dilution Agreement").

     2.   Registration under Securities Act, etc.
          --------------------------------------

          2.1  Registration on Request.
               -----------------------

               (a)  Concurrently with or from time to time after the Initial
          Registration Date, upon the written request of any Holder of
          Registrable Securities (a "Requesting Holder"), requesting that the
          Company effect the registration under the Securities Act of all or a
          portion of such Requesting Holder's Registrable Securities and
          specifying the intended method of disposition thereof and whether or
          not such requested registration is to be an underwritten offering,
          subject to the limitations set forth in subsection (e) of this Section
          2.1, the Company will use its best efforts to effect the registration
          under the Securities Act of the Registrable Securities which the
          Company has been so requested to register by the Requesting Holder
          (which request shall specify the intended method of disposition of
          such Registrable Securities), to the extent requisite to permit the
          disposition (in accordance with the intended methods thereof as
          aforesaid) of the Registrable Securities so to be registered (a
          "Demand Registration").

               (b)  Registration of Other Securities. Whenever the Company shall
                    --------------------------------
          effect a Demand Registration pursuant to this Section 2.1 in
          connection with an underwritten offering, no securities other than
          Registrable Securities shall be included among the securities covered
          by such registration unless (i) the managing underwriter of such
          offering shall have advised the Requesting Holder in writing that the
          inclusion of such other securities would not adversely affect such
          offering or (ii) the Requesting Holder shall have consented in writing
          to the inclusion of such other securities.

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               (c)  Registration Statement Form. A Demand Registration under
                    ---------------------------
          this Section 2.1 shall be on such appropriate registration form of the
          Commission (i) as shall be selected by the Company and as shall be
          reasonably acceptable to the Requesting Holder, and (ii) as shall
          permit the disposition of such Registrable Securities in accordance
          with the intended method or methods of disposition specified in the
          request for such registration. The Company agrees to include in any
          such registration statement all information which the Requesting
          Holder shall reasonably request.

               (d)  Expenses. The Company will pay all Registration Expenses in
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          connection with any Demand Registration requested pursuant to this
          Section 2.1. Selling Expenses in connection with this Section 2.1
          shall be incurred by the Requesting Holder.

               (e)  Limitations on Requested Registrations. The Company's
                    --------------------------------------
          obligation to take or continue any action to effect a Demand
          Registration under this Section 2.1 shall be subject to the following:

                    (i)   The Company shall not be required to effect a Demand
               Registration pursuant to this Section 2.1 unless the Requesting
               Holder has requested the registration of at least the lesser of
               (i) 4,300,000 Registrable Securities, adjusted for any increase
               or decrease in the number of issued shares of the Common Stock
               resulting from a stock split, reverse stock split, stock
               dividend, combination or reclassification of the Common Stock, or
               any other increase or decrease in the number of issued shares of
               Common Stock effected without consideration by the Company or
               (ii) $50 million in Fair Market Value of Registrable Securities.

                    (ii)  The Company shall not be required to effect a Demand
               Registration pursuant to this Section 2.1 more than one time in
               any twelve (12) month period.

               (f)  Selection of Underwriters. If a Demand Registration pursuant
                    -------------------------
          to this Section 2.1 involves an underwritten offering, the underwriter
          or underwriters thereof shall be selected by the Company, with the
          reasonable approval of the Requesting Holder.

          2.2  Incidental Registration.
               -----------------------

               (a)  Right to Include Registrable Securities. If the Company at
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          any time proposes to register any of its securities under the
          Securities Act (other than (i) in connection with a registration of
          any employee benefit, retirement or similar plan, or (ii) with respect
          to a transaction governed by Rule 145 under the Securities Act, or

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          (iii) pursuant to Section 2.1), whether or not for sale for its own
          account, it will each such time give prompt written notice to the
          Holders of its intention to do so and of the Holders' rights under
          this Section 2.2. Upon the written request of the any Holder made
          within thirty (30) days after the receipt of any such notice (which
          request shall specify the Registrable Securities intended to be
          disposed of and the intended method of disposition thereof), the
          Company will use its best efforts to effect the registration under the
          Securities Act of all Registrable Securities that the Company has been
          so requested to register, to the extent requisite to permit the
          disposition (in accordance with the intended methods thereof as
          aforesaid) of the Registrable Securities so to be registered, provided
                                                                        --------
          that if, at any time after giving written notice of its intention to
          register any securities and prior to the effective date of the
          registration statement filed in connection with such registration, the
          Company shall determine for any reason not to register or to delay
          registration of such securities, the Company may, at its election,
          give written notice of such determination to the Holders participating
          in such registration and, thereupon, (i) in the case of a
          determination not to register, shall be relieved of its obligation to
          register any Registrable Securities in connection with such
          registration (but not from its obligation to pay the Registration
          Expenses in connection therewith), without prejudice, however, to the
          rights of the Holders to request that such registration be effected as
          a Demand Registration under Section 2.1, and (ii) in the case of a
          determination to delay registering, shall be permitted to delay
          registering any Registrable Securities, for the same period as the
          delay in registering such other securities. No registration effected
          under this Section 2.2 shall be deemed to have been effected pursuant
          to Section 2.1 or shall relieve the Company of its obligation to
          effect any registration upon request under Section 2.1. The Company
          will pay all Registration Expenses in connection with each
          registration of Registrable Securities requested pursuant to this
          Section 2.2 and any Selling Expenses shall be incurred by the
          participating Holders.

               (b)  Priority in Incidental Registrations.
                    ------------------------------------

                    (i)   If (A) a registration pursuant to this Section 2.2
               involves an underwritten offering of the securities so being
               registered for sale for the account of a stockholder (other than
               the Holders) exercising a demand registration right pursuant to
               another registration rights agreement to be distributed (on a
               firm commitment basis) by or through one or more underwriters of
               recognized standing under underwriting terms appropriate for such
               a transaction, and (B) the managing underwriter of such
               underwritten offering informs the Company and the Holders in
               writing of its belief that the number of securities requested to
               be included in such registration exceeds the number that can be
               sold in (or during the time of) such offering, then the Company
               will include in such registration, to the extent of the number
               that the Company is so advised can be sold in (or during the time
               of) such

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               offering: first, such securities proposed by the stockholder
               exercising the demand registration right to be sold for its
               account; second, such securities requested to be included
               pursuant to incidental registration rights in such registration
               by the holder or holders, as the case may be, including the
               Holders, pro rata on the basis of the number of such securities
               so proposed to be sold by all such security holders and so
               requested to be included; and third, such securities proposed by
               the Company to be sold for its own account

                    (ii)  If (A) a registration pursuant to this Section 2.2
               involves an underwritten offering of the securities so being
               registered for sale for the account of the Company, to be
               distributed (on a firm commitment basis) by or through one or
               more underwriters of recognized standing under underwriting terms
               appropriate for such a transaction, and (B) the managing
               underwriter of such underwritten offering shall inform the
               Company and the Holders in writing of its belief that the number
               of securities requested to be included in such registration
               exceeds the number that can be sold in (or during the time of)
               such offering, then the Company will include in such
               registration, to the extent of the number that the Company is so
               advised can be sold in (or during the time of) such offering,
               securities proposed by the Company to be sold for its own
               account, and, such securities requested to be included pursuant
               to incidental registration rights in such registration by the
               holder or holders, as the case may be, including the Holders, pro
               rata on the basis of the number of such securities so proposed to
               be sold by all such security holders and so requested to be
               included.

               2.3  Registration Procedures. If and whenever the Company is
                    -----------------------
          required to use its best efforts to effect the registration of any
          Registrable Securities under the Securities Act as provided in
          Sections 2.1 and 2.2, the Company will as expeditiously as possible:

                    (a)  prepare and (as soon thereafter as possible or in any
               event no later than sixty (60) days after the end of the period
               within which requests for registration may be given to the
               Company) file with the Commission the requisite registration
               statement to effect such registration and thereafter use its best
               efforts to cause such registration statement to become effective,
               provided that the Company may discontinue any registration of its
               securities that are not Registrable Securities (and, under the
               circumstances specified in Section 2.2(a), its securities that
               are Registrable Securities) at any time prior to the effective
               date of the registration statement relating thereto;

                    (b)  prepare and file with the Commission such amendments
               and supplements to such registration statement and the prospectus
               used in connection therewith as may be necessary to keep such
               registration statement effective and to comply with the
               provisions of the Securities Act with respect to the disposition
               of all

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               securities covered by such registration statement until such time
               as all of such securities have been disposed of in accordance
               with the intended methods of disposition by the seller or sellers
               thereof set forth in such registration statement;

                    (c)  furnish to the Holders such number of conformed copies
               of such registration statement and of each such amendment and
               supplement thereto (in each case including all exhibits), such
               number of copies of the prospectus contained in such registration
               statement (including each preliminary prospectus and any summary
               prospectus) and any other prospectus filed under Rule 424 under
               the Securities Act, in conformity with the requirements of the
               Securities Act, and such other documents, as the Holders may
               reasonably request;

                    (d)  use its best efforts to register or qualify all
               Registrable Securities and other securities covered by such
               registration statement under such other securities or blue sky
               laws of such jurisdictions as the Holders shall reasonably
               request, to keep such registration or qualification in effect for
               so long as such registration statement remains in effect, and
               take any other action that may be reasonably necessary or
               advisable to enable the Holders to consummate the disposition in
               such jurisdictions of the securities owned by it, except that the
               Company shall not for any such purpose be required to qualify
               generally to do business as a foreign corporation in any
               jurisdiction wherein it would not but for the requirements of
               this subdivision (d) be obligated to be so qualified or to
               consent to general service of process in any such jurisdiction;

                    (e)  use its best efforts to cause all Registrable
               Securities covered by such registration statement to be
               registered with or approved by such other governmental agencies
               or authorities as may be necessary to enable the seller or
               sellers thereof to consummate the disposition of such Registrable
               Securities;

                    (f)  furnish to the Holders a signed counterpart, addressed
               to such seller (and underwriters, if any) of:

                         (i)   an opinion of counsel for the Company, dated the
                    effective date of such registration statement (and, if such
                    registration includes an underwritten public offering, dated
                    the date of the closing under the underwriting agreement),
                    reasonably satisfactory in form and substance to such
                    seller, and

                         (ii)  a "comfort" letter, dated the effective date of
                    such registration statement (and, if such registration
                    includes an underwritten public offering, dated the date of
                    the closing under the underwriting agreement), signed by the
                    independent public accountants who have certified the
                    Company's financial statements included in such registration
                    statement,

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               covering substantially the same matters with respect to such
               registration statement (and the prospectus included therein) and,
               in the case of the accountants' letter, with respect to events
               subsequent to the date of such financial statements, as are
               customarily covered in opinions of issuer's counsel and in
               accountants' letters delivered to the underwriters in
               underwritten public offerings of securities and, in the case of
               the accountants' letter, such other financial matters, and, in
               the case of the legal opinion, such other legal matters, as such
               seller may reasonably request;

                    (g)  notify the Holders, at any time when a prospectus
               relating thereto is required to be delivered under the Securities
               Act, upon discovery that, or upon the happening of any event as a
               result of which, the prospectus included in such registration
               statement, as then in effect, includes an untrue statement of a
               material fact or omits to state any material fact required to be
               stated therein or necessary to make the statements therein not
               misleading in the light of the circumstances under which they
               were made, and at the request of the Holders promptly prepare and
               furnish to the Holders a reasonable number of copies of a
               supplement to or an amendment of such prospectus as may be
               necessary so that, as thereafter delivered to the purchasers of
               such securities, such prospectus shall not include an untrue
               statement of a material fact or omit to state a material fact
               required to be stated therein or necessary to make the statements
               therein not misleading in the light of the circumstances under
               which they were made;

                    (h)  otherwise use its best efforts to comply with all
               applicable rules and regulations of the Commission, and make
               available to its security holders, as soon as reasonably
               practicable, an earnings statement covering the period of at
               least twelve months, but not more than eighteen months, beginning
               with the first full calendar month after the effective date of
               such registration statement, which earnings statement shall
               satisfy the provisions of Section 11(a) of the Securities Act,
               and will furnish to the Holders at least five (5) business days
               prior to the filing thereof a copy of any amendment or supplement
               to such registration statement or prospectus and shall not file
               any thereof to which the Holders shall have reasonably objected
               on the grounds that such amendment or supplement does not comply
               in all material respects with the requirements of the Securities
               Act or of the rules or regulations thereunder;

                    (i)  provide and cause to be maintained a transfer agent and
               registrar for all Registrable Securities covered by such
               registration statement from and after a date not later than the
               effective date of such registration statement;

                    (j)  use its best efforts to list all Registrable Securities
               covered by such registration statement on any securities exchange
               or automated quotation system on which any of the Registrable
               Securities is then listed; and

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                    (k)  enter into such agreements and take such other actions
               as the Holders shall reasonably request in order to expedite or
               facilitate the disposition of such Registrable Securities.

The Company may require the Holders participating in a registration to furnish
the Company such information regarding such Holder and the distribution of such
securities as the Company may from time to time reasonably request in writing.

     Each Holder agrees that upon receipt of any notice from the Company of the
happening of any event of the kind described in subdivision (g) of this Section
2.3, the Holder will forthwith discontinue its disposition of Registrable
Securities pursuant to the registration statement relating to such Registrable
Securities until the Holder's receipt of the copies of the supplemented or
amended prospectus contemplated by subdivision (g) of this Section 2.3 and, if
so directed by the Company, will deliver to the Company (at the Company's
expense) all copies, other than permanent file copies, then in the Holder's
possession of the prospectus relating to such Registrable Securities current at
the time of receipt of such notice.

               2.4  Underwritten Offerings.
                    ----------------------

                    (a)  Requested Underwritten Offerings. If requested by the
                         --------------------------------
               underwriters for any underwritten offering by a Holder pursuant
               to a Demand Registration requested under Section 2.1, the Company
               will enter into an underwriting agreement with such underwriters
               for such offering, such agreement to be reasonably satisfactory
               in substance and form to the Holder and the underwriters and to
               contain such representations and warranties by the Company and
               such other terms as are generally prevailing in agreements of
               this type, including, without limitation, indemnities to the
               effect and to the extent provided in Section 2.6. The Holder
               shall be a party to such underwriting agreement and may, at its
               option, require that any or all of the representations and
               warranties by, and the other agreements on the part of, the
               Company to and for the benefit of such underwriters shall also be
               made to and for the benefit of the Holder and that any or all of
               the conditions precedent to the obligations of such underwriters
               under such underwriting agreement be conditions precedent to the
               obligations of the Holders. The Holders shall not be required to
               make any representations or warranties to or agreements with the
               Company or the underwriters other than representations,
               warranties or agreements regarding the Holders, its Registrable
               Securities and its intended method of distribution and any other
               representation required by law.

                    (b)  Incidental Underwritten Offerings. If the Company at
                         ---------------------------------
               any time proposes to register any of its securities under the
               Securities Act whether or not for sale for its own account as
               contemplated by Section 2.2 and such securities are to be
               distributed by or through one or more underwriters, the Company
               will, if requested by the Holders as provided in Section 2.2 and
               subject to the provisions of Section

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               2.2(b), arrange for such underwriters to include all the
               Registrable Securities to be offered and sold by the Holders
               among the securities to be distributed by such underwriters. The
               participating Holders shall be a party to the underwriting
               agreement between the Company and such underwriters and may, at
               its option, require that any or all of the representations and
               warranties by, and the other agreements on the part of, the
               Company to and for the benefit of such underwriters shall also be
               made to and for the benefit of the participating Holders and that
               any or all of the conditions precedent to the obligations of such
               underwriters under such underwriting agreement be conditions
               precedent to the obligations of the Holders. The Holders shall
               not be required to make any representations or warranties to or
               agreements with the Company or the underwriters other than
               representations, warranties or agreements regarding the Holders,
               its Registrable Securities and its intended method of
               distribution and any other representation required by law.

               2.5  Preparation; Reasonable Investigation. In connection with
                    -------------------------------------
          the preparation and filing of each registration statement under the
          Securities Act pursuant to this Agreement, the Company will give the
          Holders, and their counsel and accountants, the opportunity to
          participate in the preparation of such registration statement, each
          prospectus included therein or filed with the Commission, and each
          amendment thereof or supplement thereto, and will give it such access
          to its books and records and such opportunities to discuss the
          business of the Company with its officers and the independent public
          accountants who have certified its financial statements as shall be
          necessary, in the opinion of the Holders' counsel, to conduct a
          reasonable investigation within the meaning of the Securities Act.

               2.6  Indemnification.
                    ---------------

                    (a)  Indemnification by the Company. In the event of any
                         ------------------------------
               registration of any securities of the Company under the
               Securities Act, the Company will, and hereby does, in the case of
               any registration statement filed pursuant to Section 2.1 or 2.2,
               indemnify and hold harmless the Holders, its directors and
               officers, each other Person who participates in the offering or
               sale of such securities and each other Person, if any, who
               controls any Holder within the meaning of the Securities Act
               against any losses, claims, damages or liabilities, joint or
               several, to which the Holders or any such director or officer or
               controlling person may become subject under the Securities Act or
               otherwise, insofar as such losses, claims, damages or liabilities
               (or actions or proceedings, whether commenced or threatened, in
               respect thereof) arise out of or are based upon any untrue
               statement or alleged untrue statement of any material fact
               contained in any registration statement under which such
               securities were registered under the Securities Act, any
               preliminary prospectus, final prospectus or summary prospectus
               contained therein, or any amendment or supplement thereto, or any
               omission or alleged omission to state therein a material fact
               required to be stated therein or necessary to make the statements
               therein not misleading, and the Company will reimburse the
               Holders and each such director,

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               officer, and controlling person for any legal or any other
               expenses reasonably incurred by them in connection with
               investigating or defending any such loss, claim, liability,
               action or proceeding; provided that the Company shall not be
                                     --------
               liable in any such case to the extent that any such loss, claim,
               damage, liability (or action or proceeding in respect thereof) or
               expense arises out of or is based upon an untrue statement or
               alleged untrue statement or omission or alleged omission made in
               such registration statement, any such preliminary prospectus,
               final prospectus, summary prospectus, amendment or supplement in
               reliance upon and in conformity with written information
               furnished to the Company through an instrument duly executed by a
               Holder specifically stating that it is for use in the preparation
               thereof and, provided further that the Company shall not be
                            --------
               liable to any Person who participates as an underwriter, in the
               offering or sale of Registrable Securities or any other Person,
               if any, who controls such underwriter within the meaning of the
               Securities Act, in any such case to the extent that any such
               loss, claim, damage, liability (or action or proceeding in
               respect thereof) or expense arises out of such Person's failure
               to send or give a copy of the final prospectus, as the same may
               be then supplemented or amended, to the Person asserting an
               untrue statement or alleged untrue statement or omission or
               alleged omission at or prior to the written confirmation of the
               sale of Registrable Securities to such Person if such statement
               or omission was corrected in such final prospectus. Such
               indemnity shall remain in full force and effect regardless of any
               investigation made by or on behalf of any Holder or any such
               director, officer, underwriter or controlling person and shall
               survive the transfer of such securities by such Holder.

                    (b)  Indemnification by the Holders. The Company may
                         ------------------------------
               require, as a condition to including any Registrable Securities
               in any registration statement filed pursuant to Section 2.6, that
               the Company shall have received an undertaking satisfactory to it
               from each participating Holder, to indemnify and hold harmless
               (in the same manner and to the same extent as set forth in
               subdivision (a) of this Section 2.7) the Company, each director
               of the Company, each officer of the Company and each other
               Person, if any, who controls the Company within the meaning of
               the Securities Act, with respect to any statement or alleged
               statement in or omission or alleged omission from such
               registration statement, any preliminary prospectus, final
               prospectus or summary prospectus contained therein, or any
               amendment or supplement thereto, if such statement or alleged
               statement or omission or alleged omission was made in reliance
               upon and in conformity with written information furnished to the
               Company through an instrument duly executed by the Holder
               specifically stating that it is for use in the preparation of
               such registration statement, preliminary prospectus, final
               prospectus, summary prospectus, amendment or supplement. Such
               indemnity shall remain in full force and effect, regardless of
               any investigation made by or on behalf of the Company or any such
               director, officer or controlling Person and shall survive the
               transfer of such securities by any Holder.

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                    (c)  Notices of Claims, etc. Promptly after receipt by an
                         ----------------------
               indemnified party of notice of the commencement of any action or
               proceeding involving a claim referred to in the preceding
               subdivisions of this Section 2.6, such indemnified party will, if
               a claim in respect thereof is to be made against an indemnifying
               party, give written notice to the latter of the commencement of
               such action, provided that the failure of any indemnified party
               to give notice as provided herein shall not relieve the
               indemnifying party of its obligations under the preceding
               subdivisions of this Section 2.7, except to the extent that the
               indemnifying party is actually prejudiced by such failure to give
               notice. In case any such action is brought against an indemnified
               party, unless in such indemnified party's reasonable judgment a
               conflict of interest between such indemnified and indemnifying
               parties may exist in respect of such claim, the indemnifying
               party shall be entitled to participate in and to assume the
               defense thereof, jointly with any other indemnifying party
               similarly notified to the extent that it may wish, with counsel
               reasonably satisfactory to such indemnified party, and after
               notice from the indemnifying party to such indemnified party of
               its election so to assume the defense thereof, the indemnifying
               party shall not be liable to such indemnified party for any legal
               or other expenses subsequently incurred by the latter in
               connection with the defense thereof other than reasonable costs
               of investigation. No indemnifying party shall, without the
               consent of the indemnified party, consent to entry of any
               judgment or enter into any settlement that does not include as an
               unconditional term thereof the giving by the claimant or
               plaintiff to such indemnified party of a release from all
               liability in respect to such claim or litigation.

                    (d)  Other Indemnification. Indemnification similar to that
                         ---------------------
               specified in the preceding subdivisions of this Section 2.6 (with
               appropriate modifications) shall be given by the Company and the
               Holders with respect to any required registration or other
               qualification of securities under any Federal or state law or
               regulation of any governmental authority other than the
               Securities Act.

                    (e)  Indemnification Payments. The indemnification required
                         ------------------------
               by this Section 2.6 shall be made by periodic payments of the
               amount thereof during the course of the investigation or defense,
               as and when bills are received or expense, loss, damage or
               liability is incurred.

               2.7  Adjustments Affecting Registrable Securities. The Company
                    --------------------------------------------
          will not effect or permit to occur any combination or subdivision of
          Registrable Securities which would adversely affect the ability of the
          Holders of Registrable Securities to include such Registrable
          Securities in any registration of its securities contemplated by this
          Section 2 or the marketability of such Registrable Securities under
          any such registration.

          3.   Definitions. As used herein, unless the context otherwise
               -----------
requires, the following terms have the following respective meanings:

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               Commission: The Securities and Exchange Commission or any other
               ----------
               federal agency at the time administering the Securities Act.

               Company: As defined in the introductory paragraph of this
               -------
               Agreement. For purposes of this Agreement, all references to the
               Company shall be deemed to include any successor entity or
               transferee.

               Exchange Act: The Securities Exchange Act of 1934, or any similar
               ------------
               federal statute, and the rules and regulations of the Commission
               thereunder, all as the same shall be in effect from time to time.
               Reference to a particular section of the Exchange Act shall
               include a reference to the comparable section, if any, of any
               other similar federal statute.

               Fair Market Value: With respect to a calculation of the value of
               -----------------
               Registrable Securities, the product of the number of such
               Registrable Securities and the average of the closing price of
               the Common Stock on all domestic securities exchanges on which
               such security may on the date of calculation be listed, or, if
               there have been no sales on any such exchange on the day of
               request, the average of the highest bid and lowest asked prices
               on all such exchanges at the end of such day, or, if on such day
               such security is not so listed, the average of the representative
               bid and asked prices quoted in the NASDAQ System as of 4:00 P.M.,
               New York time, on such day, or, if on any day such security is
               not quoted in the NASDAQ System, the average of the highest bid
               and lowest asked prices on such day in the domestic over-the-
               counter market as reported by the National Quotation Bureau,
               Incorporated, or any similar successor organization.

               Holder: Union Oil and any Person to which Union Oil transfers
               ------
               Registrable Securities.

               Initial Registration Date: The date that is 120 days after the
               -------------------------
               date on which the Effective Time of the Merger (each as defined
               in the Merger Agreement) occurs.

               Person: A corporation, an association, a partnership, a business,
               ------
               an individual, a governmental or political subdivision thereof or
               a governmental agency.

               Registrable Securities: Any of the Company's Common Stock issued
               ----------------------
               to Union Oil pursuant to or in connection with the Merger
               Agreement or the Non-Dilution Agreement, and any securities
               issued to issuable with respect to any such Common Stock by way
               of distribution or in connection with any reorganization,
               recapitalization, merger, consolidation or otherwise. As to any
               particular Registrable Securities, once issued such securities
               shall cease to be Registrable Securities when (a) a registration
               statement with respect to the sale of such securities shall have

                                      -11-
<PAGE>

               become effective under the Securities Act and such securities
               shall have been disposed of in accordance with such registration
               statement, (b) they shall have been distributed to the public
               pursuant to Rule 144 or Rule 144A (or any successor provision)
               under the Securities Act, (c) with respect to any Holder, the
               Registrable Securities held by such Holder represent less than 2%
               of the then issued and outstanding shares of Common Stock, such
               Holder is not an "affiliate" of the Company, and such shares may
               be sold freely by such Holder without restriction under Rule
               144(k) (or any successor provision) without restriction, or (d)
               they shall have ceased to be outstanding.

               Registration Expenses: All expenses incident to the Company's
               ---------------------
               performance of or compliance with Section 2.1 or 2.2, including,
               without limitation, all salaries of Company personnel or general
               overhead expenses of the Company, auditing fees, premiums or
               other expenses relating to liability insurance required by
               underwriters of the Company, or other expenses for the
               preparation of financial statements, all registration, filing and
               National Association of Securities Dealers fees, all fees and
               expenses of complying with securities or blue sky laws, all word
               processing, duplicating and printing expenses, messenger and
               delivery expenses, the fees and disbursements of counsel for the
               Company and of its independent public accountants, including the
               expenses of any special audits or "cold comfort" letters required
               by or incident to such performance and compliance, the fees and
               disbursements of not more than one special counsel to the holders
               of such Registrable Securities not to exceed $50,000 per
               registration, premiums and other costs of policies of insurance
               against liabilities arising out of the public offering of the
               Registrable Securities being registered and any fees and
               disbursements of underwriters customarily paid by issuers or
               sellers of securities, but excluding Selling Expenses.

               Securities Act: The Securities Act of 1933, or any similar
               --------------
               federal statute, and the rules and regulations of the Commission
               thereunder, all as of the same shall be in effect from time to
               time. References to a particular section of the Securities Act
               shall include a reference to the comparable section, if any, of
               any other similar federal statute.

               Selling Expenses: underwriting discounts and commissions and
               ----------------
               stock transfer taxes relating to securities registered by the
               Holders.

               Union Oil: As defined in the introductory paragraph of this
               ---------
               Agreement.

          4.   Rule 144 and Rule 144A: The Company will file the reports
               ----------------------
required to be filed by it under the Securities Act and the Exchange Act and the
rules and regulations adopted by the Commission thereunder (or, if the Company
is not required to file such reports, will, upon the request of any holder of
Registrable Securities, make publicly available other information) and will take
such further action as the Holders may reasonably request, all to the extent
required from time

                                      -12-
<PAGE>

to time to enable the Holders to sell Registrable Securities without
registration under the Securities Act within the limitation of the exemptions
provided by (a) Rule 144 under the Securities Act, as such rule may be amended
from time to time or (b) any similar rule or regulation hereafter adopted by the
Commission. Upon the request of any Holder, the Company will deliver to such
holder a written statement as to whether it has complied with such requirements.
After any sale of Registrable Securities pursuant to this Section 4, the Company
will, to the extent allowed by law, cause any restrictive legends to be removed
and any transfer restrictions to be rescinded with respect to such Registrable
Securities. In order to permit the Holders to sell the same, if it so desires,
pursuant to Rule 144A promulgated by the Commission (or any successor to such
rule), the Company will comply with all rules and regulations of the Commission
applicable in connection with use of Rule 144A (or any successor thereto).
Prospective transferees of Registrable Securities that are Qualified
Institutional Buyers (as defined in Rule 144A) which would be purchasing such
Registrable Securities in reliance upon Rule 144A may request from the Company
information regarding the business, operations and assets of the Company. Within
five business days of any such request, the Company shall deliver to any such
prospective transferee copies of annual audited and quarterly unaudited
financial statements of the Company and such other information as may be
required to be supplied by the Company for it to comply with Rule 144A.

          5.   Amendments and Waivers. This Agreement may be amended and the
               ----------------------
Company may take any action herein prohibited or omit to perform any act herein
required to be performed by it, only if the Company shall have obtained the
written consent to such amendment, action or omission to act, of the Holders of
a majority of the Registrable Securities. The Holders of any Registrable
Securities at the time or thereafter outstanding shall be bound by any consent
authorized by this Section 5, whether or not such Registrable Securities shall
have been marked to indicate such consent.

          6.   Nominees for Beneficial Holders. In the event that any
               -------------------------------
Registrable Securities are held by a nominee for the beneficial owner thereof,
the beneficial owner thereof may, at its election, be treated as the holder of
such Registrable Securities for purposes of this Agreement. If the beneficial
owner of any Registrable Securities so elects, the Company may require
assurances reasonably satisfactory to it of such owner's beneficial ownership of
such Registrable Securities.

          7.   Notices. All communications provided for hereunder shall be sent
               -------
by first-class mail and (a) if addressed to Union Oil, at One Sugar Creek Place,
14141 Southwest Freeway, Sugar Land, Texas 77478, Attention: Mr. Phil Ballard,
(b) if addressed to any other Holder, to the address specified by such Holder
upon its receipt of Registrable Securities, or (c) if addressed to the Company,
at 500 West Texas, Suite 200, Midland, Texas 79701 or at such other address, or
to the attention of such other officer, as the Company shall have furnished to
the Holders at the time outstanding; provided, however, that any such
communication to the Company may also, at the option of any Holder, be either
delivered to the Company at its address set forth above or to any officer of the
Company.

                                      -13-
<PAGE>

          8.   Assignment. This Agreement shall be binding upon and inure to the
               ----------
benefit of and be enforceable by the parties hereto and their respective
successors and assigns. In addition, and whether or not any express assignment
shall have been made, the provisions of this Agreement that are for the benefit
of any Holder shall also be for the benefit of and enforceable by any subsequent
holder of any Registrable Securities, subject to the provisions respecting the
minimum numbers or percentages of shares of Registrable Securities required in
order to be entitled to certain rights, or take certain actions, contained
herein.

          9.   Effectiveness; Termination. This Agreement shall become effective
               --------------------------
only upon consummation of the transactions contemplated by the Merger Agreement,
and shall terminate if the Merger Agreement is terminated in accordance with its
terms. After this Agreement becomes effective, this Agreement shall terminate
when no Registrable Securities remain outstanding.

          10.  Descriptive Headings. The descriptive headings of the several
               --------------------
sections and paragraphs of this Agreement are inserted for reference only and
shall not limit or otherwise affect the meaning hereof.

          11.  Specific Performance. The parties hereto recognize and agree that
               --------------------
money damages may be insufficient to compensate the Holders for breaches by the
Company of the terms hereof and, consequently, that the equitable remedy of
specific performance of the terms hereof will be available in the event of any
such breach.

          12.  Governing Law. THIS AGREEMENT SHALL BE CONSTRUED AND ENFORCED IN
               -------------
ACCORDANCE WITH, AND THE RIGHTS OF THE PARTIES SHALL BE GOVERNED BY, THE LAWS OF
THE STATE OF DELAWARE WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAWS.

          13.  Counterparts. This Agreement may be executed simultaneously in
               ------------
any number of counterparts, each of which shall be deemed an original, but all
such counterparts shall together constitute one and the same instrument.

                                      -14-
<PAGE>

     IN WITNESS WHEREOF, the parties have caused this Agreement to be executed
and delivered by their respective officers thereunto duly authorized as of the
date first above written.

                                        COMPANY:

                                        TITAN RESOURCES HOLDINGS, INC.

                                        By:  /s/ Phillip Ballard
                                             -------------------------------
                                             Phillip Ballard
                                             Vice President

                                        UNION OIL COMPANY OF CALIFORNIA

                                        By:  /s/ Timothy H. Ling
                                             -------------------------------
                                             Timothy H. Ling
                                             Executive Vice President, North
                                             American Energy Operations and
                                             Chief Financial Officer

                                      -15-<PAGE>

                                                                    Exhibit 10.3

                              1999 INCENTIVE PLAN

                                      of

                              PURE RESOURCES, INC.

           1.    Plan.  This 1999 Incentive Plan of Pure Resources, Inc. (the
"Plan") was adopted by the Board of Directors of Pure Resources, Inc. (formerly
Titan Resources Holdings, Inc.), a Delaware corporation (the "Company"), to
reward certain officers and other key employees of the Company and its
subsidiaries by enabling them to acquire shares of Common Stock, par value $.01
per share, of the Company and/or to be compensated for individual performance.

           2.    Objectives. The Plan is designed to attract and retain officers
and other key employees of the Company and its Subsidiaries (as hereinafter
defined), to encourage a sense of proprietorship of such persons and to
stimulate the active interest of such persons in the development and financial
success of the Company and its Subsidiaries. These objectives are to be
accomplished by making Awards (as hereinafter defined) under the Plan, thereby
providing Participants (as hereinafter defined) with a proprietary interest in
the growth and performance of the Company and its Subsidiaries.

           3.    Definitions.  As used herein, the terms set forth below shall
have the following respective meanings:

                 (a)   "Authorized Officer" means the Chairman of the Board or
     the Chief Executive Officer of the Company (or any other senior officer of
     the Company to whom either of them shall delegate the authority to execute
     any Award Agreement).

                 (b)   "Award" means the grant of any Option, SAR, Stock Award,
     Cash Award or Performance Award, whether granted singly, in combination or
     in tandem, to a Participant pursuant to such applicable terms, conditions
     and limitations as the Committee may establish in order to fulfill the
     objectives of the Plan.

                 (c)   "Award Agreement" means a written agreement between the
     Company and a Participant setting forth the terms, conditions and
     limitations applicable to an Award.

                 (d)   "Board" means the Board of Directors of the Company.

                 (e)   "Cash Award" means an award denominated in cash.

                 (g)   "Code" means the Internal Revenue Code of 1986, as
     amended from time to time.

                 (h)   "Committee" means the committee designated by the Board
     pursuant to Paragraph 6(a) to administer the Plan.
<PAGE>

                 (i)   "Common Stock" means the Common Stock, par value $.01 per
     share, of the Company.

                 (j)   "Common Stock Equivalents" means (without duplication
     with any other Common Stock or Common Stock Equivalents) rights, warrants,
     options, convertible securities, exchangeable securities or indebtedness,
     or other rights, exercisable for or convertible or exchangeable into,
     directly or indirectly, Common Stock or securities convertible or
     exchangeable into Common Stock, whether at the time the number of shares of
     Common Stock Equivalents are determined or within sixty days of that date
     and that are traded or are of the same class as securities that are traded
     on a national securities exchange or quoted on the NASDAQ National Market
     System, NASDAQ, or National Quotation Bureau Incorporated. The number of
     shares of Common Stock Equivalents outstanding shall equal the number of
     shares of Common Stock plus the number of shares of Common Stock issuable
     upon exercise, conversion or exchange of all other Common Stock
     Equivalents.

                 (k)   "Company" means Pure Resources, Inc. (formerly Titan
     Resources Holdings, Inc.), a Delaware corporation.

                 (l)   "Dividend Equivalents" means, with respect to shares of
     Restricted Stock that are to be issued at the end of the Restriction
     Period, an amount equal to all dividends and other distributions (or the
     economic equivalent thereof) that are payable to stockholders of record
     during the Restriction Period on a like number of shares of Common Stock.

                 (m)   "Effective Date" has the meaning set forth in Paragraph
     24 hereof.

                 (n)   "Employee" means an employee of the Company or any of its
     Subsidiaries, and may include an individual who is expected to become an
     employee of the Company or one of its Subsidiaries; provided, however, that
     an Award made under the Plan to an individual who is expected to become an
     employee shall be forfeited in the event that the individual does not
     become an employee of the Company or one of its Subsidiaries within the
     six-month period following the date on which the Award is granted.

                 (o)   "Exchange Act" means the Securities Exchange Act of 1934.

                 (p)   "Fair Market Value" of a share of Common Stock means, as
     of a particular date, (i) if shares of Common Stock are listed on a
     national securities exchange, the closing sales price per share of Common
     Stock on the consolidated transaction reporting system for the principal
     national securities exchange on which shares of Common Stock are listed on
     that date, or, if there shall have been no such sale so reported on that
     date, on the last preceding date on which such a sale was so reported, (ii)
     if shares of Common Stock are not so listed but are quoted on the NASDAQ
     National Market System, the closing sales price per share of Common Stock
     reported by the NASDAQ National Market System on that date, or, if there
     shall have been no such sale so reported on that date, on the last
     preceding date

                                      -2-
<PAGE>

     on which such a sale was so reported, (iii) if the Common Stock is not so
     listed or quoted, the average of the closing bid and asked price on that
     date, or, if there are no quotations available for such date, on the last
     preceding date on which such quotations shall be available, as reported by
     the NASDAQ National Market System, or, if not reported by the NASDAQ
     National Market System, by the National Quotation Bureau Incorporated or
     (iv) if shares of Common Stock are not publicly traded, the most recent
     value determined by an independent appraiser appointed by the Company for
     such purpose.

                 (q)   "Fundamental Change" has the meaning set forth in
     Paragraph 13.

                 (r)   "NASDAQ" means the National Association of Securities
     Dealers, Inc. Automated Quotations, Inc.

                 (s)   "Option" means a right to purchase a specified number of
     shares of Common Stock at a specified price.  All Options granted pursuant
     to the Plan shall be nonqualified stock options that are not intended to
     comply with the requirements set forth in Section 422 of the Code.

                 (t)   "Participant" means an Employee to whom an Award has been
     made under the Plan.

                 (u)   "Performance Award" means an Award representing a
     contingent right to receive a specified amount of cash or shares of Common
     Stock upon the attainment of one or more Performance Goals.

                 (v)   "Performance Goal" means a standard established by the
     Committee to determine in whole or in part whether a Performance Award
     shall be earned.

                 (w)   "Restricted Stock" means Common Stock that is
     nontransferable or subject to a substantial risk of forfeiture until
     specific conditions are satisfied.

                 (x)   "Restriction Period" means a period of time beginning as
     of the date upon which Restricted Stock is transferred to a Participant
     pursuant to the Plan and ending as of the date upon which the Common Stock
     subject to such Award is no longer nontransferable or subject to a
     substantial risk of forfeiture.

                 (y)   "SAR" means a right to receive a payment, in cash or
     Common Stock, equal to the excess of the Fair Market Value or other
     specified valuation of a specified number of shares of Common Stock on the
     date the right is exercised over a specified strike price, in each case, as
     determined by the Committee.

                 (z)   "Stock Award" means an Award in the form of shares of
     Common Stock or units denominated in shares of Common Stock.

                                      -3-
<PAGE>

                 (aa)  "Subsidiary" means (i) in the case of a corporation, any
     corporation in which the Company directly or indirectly owns shares
     representing more than 50% of the combined voting power of the shares of
     all classes or series of capital stock of such corporation which have the
     right to vote generally on matters submitted to a vote of the stockholders
     of such corporation and (ii) in the case of a partnership or other business
     entity not organized as a corporation, any such business entity of which
     the Company directly or indirectly owns more than 50% of the voting,
     capital or profits interests (whether in the form of partnership interests,
     membership interests or otherwise).

           4.    Eligibility. Employees who hold positions of responsibility and
whose performance, in the judgment of the Committee, can have a significant
effect on the success of the Company and its Subsidiaries are eligible to
receive Awards under the Plan.

           5.    Common Stock Available for Awards.

                 (a)   Maximum Number of Shares.  Subject to the provisions of
     Paragraph 14 hereof, there shall be available for Awards under the Plan
     granted wholly or partly in Common Stock (including rights or options that
     may be exercised for or settled in Common Stock) an aggregate number of
     shares of Common Stock equal to (a) twelve percent of the total number of
     shares of Common Stock Equivalents outstanding from time to time minus (b)
     the total number of  shares of Common Stock subject to outstanding awards
     on the date of calculation under any other stock-based plan for employees
     of the Company and its Subsidiaries.

                 (b)   Determination of Available Shares. The Committee may from
     time to time adopt and observe such procedures concerning the counting of
     shares against the Plan maximum as it may deem appropriate.

                 (c)   Restoration of Unused and Surrendered Shares. The number
     of shares of Common Stock that are subject to Awards under the Plan, that
     are forfeited or terminated, expire unexercised, are settled in cash in
     lieu of Common Stock or in a manner such that all or some of the shares
     covered by an Award are not issued to a Participant or are exchanged for
     Awards that do not involve Common Stock, shall again immediately become
     available for Awards hereunder.

                 (d)   Description of Shares. The shares to be delivered under
     the Plan shall be made available from (a) authorized but unissued shares of
     Common Stock, (b) Common Stock held in the treasury of the Company, or (c)
     previously issued shares of Common Stock reacquired by the Company,
     including shares purchased on the open market, in each situation as the
     Board or the Committee may determine from time to time at its sole option.

                 (e)   Registration and Listing of Shares.  The Board and the
     appropriate officers of the Company shall from time to time take whatever
     actions are necessary to file any required documents with governmental
     authorities, stock exchanges and transaction

                                      -4-
<PAGE>

     reporting systems to ensure that shares of Common Stock are available for
     issuance pursuant to Awards.

           6.    Administration.

                 (a)   Committee.  The Plan shall be administered by the
     Compensation Committee or such other committee of the Board designated by
     the Board to administer the Plan; provided, however, that the Committee
     shall be constituted in a manner that satisfies the requirements of Rule
     16b-3 under Section 16(b) of the Exchange Act, which Committee shall
     administer the Plan with respect to all Employees who are subject to
     Section 16 of the Exchange Act in a manner that satisfies the requirements
     of Rule 16b-3 under Section 16(b) of the Exchange Act.  The number of
     persons that shall constitute the Committee shall be determined from time
     to time by a majority of all the members of the Board.  The members of the
     Committee shall serve at the pleasure of the Board, which shall have the
     power, at any time and from time to time, to remove members from or add
     members to the Committee. Removal from the Committee may be with or without
     cause.  Any individual serving as a member of the Committee shall have the
     right to resign from membership in the Committee by written notice to the
     Board.  The Board, and not the remaining members of the Committee, shall
     have the power and authority to fill vacancies on the Committee, however
     caused.

                 (b)   Meetings and Actions of Committee.  The Board  shall
     designate which of the Committee members shall be the chairman of the
     Committee.  If the Board fails to designate a Committee chairman, the
     members of the Committee shall elect one of the Committee members as
     chairman, who shall act as chairman until he ceases to be a member of the
     Committee or until the Board  or the Committee elects a new chairman.  The
     Committee shall hold its meetings at those times and places as the chairman
     of the Committee may determine.  At all meetings of the Committee, a quorum
     for the transaction of business shall be required, and a quorum shall be
     deemed present if at least a majority of the members of the Committee are
     present.  At any meeting of the Committee, each member shall have one vote.
     All decisions and determinations of the Committee shall be made by the
     majority vote or majority decision of all of its members present at a
     meeting at which a quorum is present; provided, however, that any decision
     or determination reduced to writing and signed by all of the members of the
     Committee shall be as fully effective as if it had been made at a meeting
     that was duly called and held.  The Committee may make any rules and
     regulations as it may deem advisable for the conduct of its business that
     are not inconsistent with the provisions of the Plan, the Certificate of
     Incorporation, the by-laws of the Company, Rule 16b-3 under Section 16 of
     the Exchange Act so long as it is applicable.

                 (c)   Powers of Committee. Subject to the provisions hereof,
     the Committee shall have full and exclusive power and authority to
     administer the Plan and to take all actions that are specifically
     contemplated hereby or are necessary or appropriate in connection with the
     administration hereof. The Committee shall also have full and exclusive
     power to interpret the Plan and to adopt such rules, regulations and
     guidelines for carrying

                                      -5-
<PAGE>

     out the Plan as it may deem necessary or proper, all of which powers shall
     be exercised in the best interests of the Company and in keeping with the
     objectives of the Plan. The Committee may, in its discretion, provide for
     the extension of the exercisability of an Award, accelerate the vesting or
     exercisability of an Award, eliminate or make less restrictive any
     restrictions contained in an Award, waive any restrictions or other
     provision of the Plan or an Award or otherwise amend or modify an Award in
     any manner that is either (i) not adverse to the Participant to whom such
     Award was granted or (ii) consented to by such Participant. The Committee
     may correct any defect or supply any omission or reconcile any
     inconsistency in the Plan or in any Award in the manner and to the extent
     the Committee deems necessary or desirable to further the Plan purposes.
     Any decision of the Committee in the interpretation and administration of
     the Plan shall lie within its sole and absolute discretion and shall be
     final, conclusive and binding on all parties concerned.

           (d)   Delegation of Authority. The Committee may delegate to the
     Chief Executive Officer and to other senior officers of the Company its
     duties under the Plan pursuant to such conditions or limitations as the
     Committee may establish.

           (e)   Liability. No member of the Committee or officer of the Company
     to whom the Committee has delegated authority in accordance with the
     provisions of Subparagraph (d) above shall be liable for anything done by
     him or her, by any member of the Committee or by any officer of the Company
     in connection with the performance of any duties under the Plan, except for
     his or her own willful fraud or as expressly provided by statute.

           7.    Awards.  The Committee shall determine the type or types of
Awards to be made under the Plan and shall designate from time to time the
Employees who are to be the recipients of such Awards.  Each Award may be
embodied in an Award Agreement, which shall contain such terms, conditions and
limitations as shall be determined by the Committee in its sole discretion and
shall be signed by the Participant to whom the Award is made and by an
Authorized Officer for and on behalf of the Company.  Awards may consist of
those listed in this Paragraph 7 and may be granted singly, in combination or in
tandem.  Awards may also be made in combination or in tandem with, in
replacement of, or as alternatives to, grants or rights under the Plan or any
other employee plan of the Company or any of its Subsidiaries, including the
plan of any acquired entity. The terms and provisions of the respective Award
Agreements need not be identical.  An Award may provide for the grant or
issuance of additional, replacement or alternative Awards upon the occurrence of
specified events, including the exercise of the original Award granted to a
Participant. All or part of an Award may be subject to conditions established by
the Committee, which may include, but are not limited to, continuous service
with the Company and its Subsidiaries, achievement of specific business
objectives, increases in specified indices, attainment of specified growth rates
and other comparable measurements of performance.  Unless otherwise specified in
the Plan, upon the termination of employment of a Participant, any unexercised,
deferred, unvested or unpaid Awards shall be treated as set forth in the
applicable Award Agreement.

           (a)   Options.

                                      -6-
<PAGE>

                 (i)   An Award may be in the form of an Option. The price at
           which shares of Common Stock may be purchased upon the exercise of an
           Option shall be not less than the greater of (i) 25 percent of the
           Fair Market Value of the Common Stock on the date of grant or (ii)
           its par value.

                 (ii)  The term of each Option shall be as specified by the
           Committee; provided, however, that unless otherwise designated by the
           Committee, no Option shall be exercisable later than 10 years from
           the effective date of the Option's grant.

                 (iii) Each Award Agreement embodying an Option shall set forth
           the extent to which the Participant shall have the right to exercise
           the Option following the Participant's termination of employment with
           the Company or a Subsidiary. Such provisions shall be determined in
           the sole discretion of the Committee, need not be uniform among all
           Options granted under the Plan and may reflect distinctions based on
           the reasons for termination of employment. In the event that a
           Participant's Award Agreement embodying an Option does not set forth
           such termination provisions, the following termination provisions
           shall apply with respect to such Option:

                       (A)   Death or Disability. If the employment of a
                 Participant shall terminate by reason of death or permanent and
                 total disability (within the meaning of Section 22(e)(3) of the
                 Code), outstanding Options held by the Participant may be
                 exercised, to the extent then vested, no more than one year
                 from the date of such termination of employment, unless the
                 Options, by their terms, expire earlier.

                       (B)   Other Termination. If the employment or service of
                 a Participant shall terminate for a reason other than the
                 reasons set forth in subparagraph (A) above, whether on a
                 voluntary or involuntary basis, outstanding Options held by the
                 Participant may be exercised, to the extent then vested, no
                 more than three months from the date of such termination of
                 employment, unless the Options, by their terms, expire earlier.

                       (C)   Termination for Cause. Notwithstanding
                 subparagraphs (A) and (B) above, if the employment of a
                 Participant shall be terminated by reason of such Participant's
                 fraud against the Company or a Subsidiary or conviction of a
                 felony, all outstanding Options held by the Participant shall
                 immediately be forfeited to the Company and no additional
                 exercise period shall be allowed, regardless of the vested
                 status of the Options.

     Subject to the foregoing provisions, the terms, conditions and limitations
     applicable to any Options awarded pursuant to the Plan, including the term
     of any Options and the date or dates upon which they become exercisable,
     shall be determined by the Committee.

                                      -7-
<PAGE>

           (b)   Stock Appreciation Right. An Award may be in the form of an
     SAR. The terms, conditions and limitations applicable to any SARs awarded
     pursuant to the Plan, including the term of any SARs and the date or dates
     upon which they become exercisable, shall be determined by the Committee.

           (c)   Stock Award. An Award may be in the form of a Stock Award. The
     terms, conditions and limitations applicable to any Stock Awards granted
     pursuant to the Plan shall be determined by the Committee.

           (d)   Cash Award. An Award may be in the form of a Cash Award. The
     terms, conditions and limitations applicable to any Cash Awards granted
     pursuant to the Plan shall be determined by the Committee.

           (e)   Performance Award. Without limiting the type or number of
     Awards that may be made under the other provisions of the Plan, an Award
     may be in the form of a Performance Award. A Performance Award shall be
     paid, vested or otherwise deliverable solely on account of the attainment
     of one or more pre-established, objective Performance Goals established by
     the Committee.

           8.    Payment of Awards.

           (a)   General.  Payment of Awards may be made in the form of cash or
     Common Stock, or a combination thereof, and may include such restrictions
     as the Committee shall determine, including, in the case of Common Stock,
     restrictions on transfer and forfeiture provisions.  If payment of an Award
     is made in the form of Restricted Stock, the Award Agreement relating to
     such shares shall specify whether they are to be issued at the beginning or
     end of the Restriction Period.  In the event that shares of Restricted
     Stock are to be issued at the beginning of the Restriction Period, the
     certificates evidencing such shares (to the extent that such shares are so
     evidenced) shall contain appropriate legends and restrictions that describe
     the terms and conditions of the restrictions applicable thereto.  In the
     event that shares of Restricted Stock are to be issued at the end of the
     Restriction Period, the right to receive such shares shall be evidenced by
     book entry registration or in such other manner as the Committee may
     determine.

           (b)   Deferral. With the approval of the Committee, payments in
     respect of Awards may be deferred, either in the form of installments or a
     future lump-sum payment. The Committee may permit selected Participants to
     elect to defer payments of some or all types of Awards in accordance with
     procedures established by the Committee. Any deferred payment of an Award,
     whether elected by the Participant or specified by the Award Agreement or
     by the Committee, may be forfeited if and to the extent that the Award
     Agreement so provides.

           (c)   Dividends and Interest.  Rights to dividends or Dividend
     Equivalents may be extended to and made part of any Award consisting of
     shares of Common Stock or units

                                      -8-
<PAGE>

     denominated in shares of Common Stock, subject to such terms, conditions
     and restrictions as the Committee may establish. The Committee may also
     establish rules and procedures for the crediting of interest on deferred
     cash payments and Dividend Equivalents for Awards consisting of shares of
     Common Stock or units denominated in shares of Common Stock.

           (d)   Substitution of Awards.  At the discretion of the Committee, a
     Participant may be offered an election to substitute an Award for another
     Award or Awards of the same or different type.

           9.    Stock Option Exercise.

           (a)   Subject to the terms and conditions of the Plan, Options shall
     be exercised by the delivery of a written notice of exercise to the
     Company, setting forth the number of shares of Common Stock with respect to
     which the Option is to be exercised, accompanied by full payment for such
     shares.

           (b)   The price at which shares of Common Stock may be purchased
     under an Option shall be paid in full at the time of exercise (i) in cash
     or (ii) if elected by the Participant, the Participant may purchase such
     shares by means of tendering Common Stock or surrendering another Award,
     including Restricted Stock, valued at Fair Market Value on the date of
     exercise, or any combination thereof. The Committee shall determine
     acceptable methods for Participants to tender Common Stock or other Awards.
     The Committee may provide for procedures to permit the exercise or purchase
     of such Awards by use of the proceeds to be received from the sale of
     Common Stock issuable pursuant to an Award. Unless otherwise provided in
     the applicable Award Agreement, in the event shares of Restricted Stock are
     tendered as consideration for the exercise of an Option, a number of the
     shares issued upon the exercise of the Option, equal to the number of
     shares of Restricted Stock used as consideration therefor, shall be subject
     to the same restrictions as the Restricted Stock so submitted as well as
     any additional restrictions that may be imposed by the Committee.

           (c)   Payment of the exercise price of an Option may also be made, in
     the discretion of the Committee, by delivery to the Company or its
     designated agent of an executed irrevocable option exercise form together
     with irrevocable instructions to a broker-dealer to sell or margin a
     sufficient portion of the shares with respect to which the Option is
     exercised and deliver the sale or margin loan proceeds directly to the
     Company to pay the exercise price and any required withholding taxes.

           (d)   The Committee, in its sole and absolute discretion, may approve
     the extension of a loan to a Participant by the Company to assist the
     Participant in paying the exercise price of an Option and/or any tax
     required by law to be withheld upon exercise of an Option; provided,
     however, that a Participant shall be required to pay in cash the par value
     of Common Stock received upon exercise of an Option.   Any such loan shall
     be made upon

                                      -9-
<PAGE>

     such terms and conditions (including interest rate, security and terms of
     repayment) as may be determined by the Committee in its discretion and
     applicable law.

           (e)   As soon as reasonably practicable after receipt of written
     notification of exercise of an Option and full payment of the exercise
     price and any required withholding taxes, the Company shall deliver to the
     Participant, in the Participant's name, a stock certificate or certificates
     in an appropriate amount based upon the number of shares of Common Stock
     purchased under the Option.

           10.   Tax Withholding.  The Company shall have the right to deduct
applicable taxes from any Award payment and withhold, at the time of delivery or
vesting of cash or shares of Common Stock under the Plan, an appropriate amount
of cash or number of shares of Common Stock or a combination thereof for payment
of taxes required by law or to take such other action as may be necessary in the
opinion of the Company to satisfy all obligations for withholding of such taxes.
The Committee may also permit withholding to be satisfied by the transfer to the
Company of shares of Common Stock theretofore owned by the holder of the Award
with respect to which withholding is required.  If shares of Common Stock are
used to satisfy tax withholding, such shares shall be valued based on the Fair
Market Value when the tax withholding is required to be made. The Committee may
provide for loans, on either a short-term or demand basis, from the Company to a
Participant to permit the payment of taxes required by law.

           11.   Amendment, Modification, Suspension or Termination.  The Board
may amend, modify, suspend or terminate the Plan for the purpose of meeting or
addressing any changes in legal requirements or for any other purpose permitted
by law, except that no amendment or alteration that would adversely affect the
rights of any Participant under any Award previously granted to such Participant
shall be made without the consent of such Participant.

           12.   Assignability.  Except as otherwise provided in a Participant's
Award Agreement, no Award granted under the Plan may be sold, transferred,
pledged, exchanged, hypothecated or otherwise disposed of, other than by will or
pursuant to the applicable laws of descent and distribution.  Further, no Award
shall be subject to execution, attachment or similar process.  Any attempted
sale, transfer, pledge, exchange, hypothecation or other disposition of an Award
not specifically permitted by the Plan or the Award Agreement shall be null and
void and without effect.  Except as otherwise provided in an Award Agreement,
Awards granted to a Participant under the Plan shall be exercisable during his
or her lifetime only by such Participant or, in the event of the Participant's
legal incapacity, by his or her guardian or legal representative.

           13.   Fundamental Change.  Except as otherwise provided in an Award
Agreement, if (i) the Company enters into any merger, consolidation or
recapitalization pursuant to which the persons serving as directors of the
Company immediately before such transaction cease to constitute at least 40% of
the members of the board of directors of the surviving entity (whether the
Company or another entity) following consummation of such transaction, (ii) the
Company sells, leases or exchanges or agrees to sell, lease or exchange all or
substantially all of its assets to any other person or entity, or (iii) the
Company is to be dissolved and liquidated (each such event is referred to herein

                                      -10-
<PAGE>

as a "Fundamental Change"), then immediately before the consummation of the
Fundamental Change --

           (a)   any portion of an Option which has not then vested shall become
     vested and the Company, at its discretion, shall either (i) provide to the
     Participant at least 30 days' notice of such pending Fundamental Change so
     as to permit the Participant to exercise the Option before consummation of
     such Fundamental Change, in which case the Company need not make provision
     for an Award to survive the consummation of such Fundamental Change, or
     (ii) make or cause to be made lawful and adequate provision whereby, upon
     the due exercise of the Option after the effective date of such Fundamental
     Change, the Participant shall be entitled to purchase upon exercise of the
     Option, the number and class of shares or other securities or property to
     which the Participant would have been entitled pursuant to the terms of the
     Fundamental Change if, immediately before consummation of such Fundamental
     Change, the Participant had been the holder of record of the number of
     shares of Common Stock which could be purchased upon exercise of the Option
     immediately before such Fundamental Change;

           (b)   the restriction period of any Restricted Stock shall
     immediately be accelerated and the restrictions shall expire; and

           (c)   the target payout opportunity attainable under any Performance
     Awards will be deemed to have been fully earned for all performance periods
     upon the occurrence of the Fundamental Change and the Participant will be
     paid a pro rata portion of all associated targeted payout opportunities
     (based on the number of complete and partial calendar months elapsed as of
     the occurrence of the Fundamental Change) in cash within ten days following
     the Fundamental Change or in Common Stock effective as of the date of the
     Fundamental Change, for cash and stock-based Performance Awards,
     respectively.

This Paragraph shall not impose on a Participant the obligation to exercise any
Award immediately before or upon the Fundamental Change, and, except as provided
in subparagraph (a)(i) above, a Participant shall not forfeit the right to
exercise an Award during the remainder of the original term of the Award because
of a Fundamental Change.  Notwithstanding any provision of this Plan to the
contrary, a "Fundamental Change" shall not include the merger of TRH, Inc. with
into Titan Exploration, Inc. pursuant to the terms of the Agreement and Plan of
Merger dated as of December 13, 1999, by and among Union Oil Company of
California, the Company, TRH, Inc., and Titan Exploration, Inc.

           14.   Adjustments.

           (a)   The existence of outstanding Awards shall not affect in any
     manner the right or power of the Company or its stockholders to make or
     authorize any or all adjustments, recapitalizations, reorganizations or
     other changes in the capital stock of the Company or its business or any
     merger or consolidation of the Company, or any issue of bonds, debentures,
     preferred or prior preference stock (whether or not such issue is prior to,
     on a parity with or

                                      -11-
<PAGE>

     junior to the Common Stock) or the dissolution or liquidation of the
     Company, or any sale or transfer of all or any part of its assets or
     business, or any other corporate act or proceeding of any kind, whether or
     not of a character similar to that of the acts or proceedings enumerated
     above.

           (b)   In the event of any subdivision or consolidation of outstanding
     shares of Common Stock, declaration of a dividend payable in shares of
     Common Stock or other stock split, then (i) the number of shares of Common
     Stock reserved under the Plan, (ii) the number of shares of Common Stock
     covered by outstanding Awards in the form of Common Stock or units
     denominated in Common Stock, (iii) the exercise or other price in respect
     of such Awards and (iv) the appropriate Fair Market Value and other price
     determinations for such Awards shall each be proportionately adjusted by
     the Board to reflect such transaction. In the event of any other
     recapitalization or capital reorganization of the Company, any
     consolidation or merger of the Company with another corporation or entity,
     the adoption by the Company of any plan of exchange affecting the Common
     Stock or any distribution to holders of Common Stock of securities or
     property (other than normal cash dividends or dividends payable in Common
     Stock), the Board shall make appropriate adjustments to (i) the number of
     shares of Common Stock covered by Awards in the form of Common Stock or
     units denominated in Common Stock, (ii) the exercise or other price in
     respect of such Awards and (iii) the appropriate Fair Market Value and
     other price determinations for such Awards to give effect to such
     transaction shall each be proportionately adjusted by the Board to reflect
     such transaction; provided that such adjustments shall only be such as are
     necessary to maintain the proportionate interest of the holders of the
     Awards and preserve, without exceeding, the value of such Awards.  In the
     event of a corporate merger, consolidation, acquisition of property or
     stock, separation, reorganization or liquidation, the Board shall be
     authorized to issue or assume Awards by means of substitution of new
     Awards, as appropriate, for previously issued Awards or to assume
     previously issued Awards as part of such adjustment.

           15.   Restrictions. No Common Stock or other form of payment shall be
issued with respect to any Award unless the Company shall be satisfied based on
the advice of its counsel that such issuance will be in compliance with
applicable federal and state securities laws. Certificates evidencing shares of
Common Stock delivered under the Plan (to the extent that such shares are so
evidenced) may be subject to such stop transfer orders and other restrictions as
the Committee may deem advisable under the rules, regulations and other
requirements of the Securities and Exchange Commission, any securities exchange
or transaction reporting system upon which the Common Stock is then listed or to
which it is admitted for quotation and any applicable federal or state
securities law. The Committee may cause a legend or legends to be placed upon
such certificates (if any) to make appropriate reference to such restrictions.

           16.   Unfunded Plan. Insofar as it provides for Awards of cash,
Common Stock or rights thereto, the Plan shall be unfunded. Although bookkeeping
accounts may be established with respect to Participants who are entitled to
cash, Common Stock or rights thereto under the Plan, any such accounts shall be
used merely as a bookkeeping convenience. The Company shall not be

                                      -12-
<PAGE>

required to segregate any assets that may at any time be represented by cash,
Common Stock or rights thereto, nor shall the Plan be construed as providing for
such segregation, nor shall the Company, the Board or the Committee be deemed to
be a trustee of any cash, Common Stock or rights thereto to be granted under the
Plan. Any liability or obligation of the Company to any Participant with respect
to an Award of cash, Common Stock or rights thereto under the Plan shall be
based solely upon any contractual obligations that may be created by the Plan
and any Award Agreement, and no such liability or obligation of the Company
shall be deemed to be secured by any pledge or other encumbrance on any property
of the Company. Neither the Company nor the Board nor the Committee shall be
required to give any security or bond for the performance of any obligation that
may be created by the Plan.

           17.   No Fractional Shares. No fractional shares of Common Stock
shall be issued pursuant to any Award granted under the Plan, and no payment or
other adjustment shall be made in respect of any such fractional share.

           18.   Binding Effect.  The obligation of the Company under the Plan
shall be binding upon any successor corporation or organization resulting from
the merger, consolidation or other reorganization of the Company, or upon any
successor corporation or organization succeeding to all or substantially all of
the assets and business of the Company.  The terms and conditions of the Plan
shall be binding upon each Participant and his or her heirs, legatees,
distributees and legal representatives.

           19.   Risk of Participation.  Nothing contained in the Plan shall be
construed either as a guarantee by the Company or its Subsidiaries, or their
respective stockholders, directors, officers or employees, or the value of any
assets of the Plan or as an agreement by the Company or its Subsidiaries, or
their respective stockholders, directors, officers or employees, to indemnify
anyone for any losses, damages, costs or expenses resulting from participation
in the Plan.

           20.   No Guarantee of Tax Consequences.  No person connected with the
Plan in any capacity, including, but not limited to, the Company and its
Subsidiaries and their respective directors, officers, agents and employees,
makes any representation, commitment or guarantee that any tax treatment,
including, but not limited to, federal, state and local income, estate and gift
tax treatment, will be applicable with respect to any Awards or payments
thereunder made to or for the benefit of a Participant under the Plan or that
such tax treatment will apply to or be available to a Participant on account of
participation in the Plan.

           21.   Continued Employment.  Nothing contained in the Plan or in any
Award Agreement shall confer upon any Participant the right to continue in the
employ of the Company, or interfere in any way with the rights of the Company to
terminate his or her employment at any time, with or without cause.

           22.   Miscellaneous. Headings are given to the articles and sections
of the Plan solely as a convenience to facilitate reference. Such headings shall
not be deemed in any way material or relevant to the construction of the Plan or
any provisions hereof. The use of the

                                      -13-
<PAGE>

masculine gender shall also include within its meaning the feminine. Wherever
the context of the Plan dictates, the use of the singular shall also include
within its meaning the plural, and vice versa.

           23.   Governing Law. The Plan and all determinations made and actions
taken pursuant hereto, to the extent not otherwise governed by mandatory
provisions of the Code or the securities laws of the United States, shall be
governed by and construed in accordance with the laws of the State of Delaware.

           24.   Effectiveness.  The Plan shall be effective as of December 13,
1999, the date of its adoption by the Board, provided (i) it is duly approved by
the holders of at least a majority of the shares of Common Stock in accordance
with applicable law within twelve months after the date of adoption of the Plan
by the Board and (ii) the transactions contemplated by the Agreement and Plan of
Merger dated as of December 13, 1999, by and among Union Oil Company of
California, the Company, TRH, Inc., and Titan Exploration, Inc. are consummated.
If the Plan is not so approved or such transactions are not so consummated, the
Plan shall terminate and any Awards granted hereunder shall be null and void.

                                      -14-
<PAGE>

     IN WITNESS WHEREOF, this Plan has been executed to be effective as of the
13th day of December, 1999.

                                       PURE RESOURCES, INC.

                                       By: /s/ Barry Hoffman
                                           ---------------------------
                                           Name:   Barry A. L. Hoffman
                                           Title:  Vice President

                                      -15-

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