<PAGE>

                                                                    EXHIBIT 10.3

               INSURANCE ALLOCATION AND ADMINISTRATION AGREEMENT


                                 by and among

                     COLUMBIA/HCA HEALTHCARE CORPORATION,


                                      and


                             TRIAD HOSPITALS, INC.


                                      and


                           LIFEPOINT HOSPITALS, INC.



                           dated as of May 11, 1999
<PAGE>

                               TABLE OF CONTENTS

<TABLE>
<S>                                                                          <C>
Section 1.  Allocation of Existing Coverages and Liabilities...............  2
Section 2.  Cooperation and Joint Insurance................................  3
Section 3.  Administrative Services........................................  4
Section 4.  Amendment of Policies..........................................  4
Section 5.  Access to Records and Other Information........................  5
Section 6.  Successors and Assigns.........................................  5
Section 7.  Counterparts...................................................  5
Section 8.  Governing Law..................................................  5
Section 9.  No Impairments of Other Rights.................................  5
Section 10  Subrogation....................................................  5
Section 11. Subsidiaries...................................................  6
Section 12. No Third Party Beneficiaries...................................  6
Section 13. Construction...................................................  6
Section 14. Entire Agreement; Amendment....................................  6
Section 15. Waivers........................................................  6
Section 16. Confidentiality................................................  7
Section 17. Notices........................................................  7
Section 18. Legal Enforceability...........................................  9
Section 19. Survival of Agreements.........................................  9
</TABLE>
<PAGE>

          This Insurance Allocation and Administration Agreement (the
"Agreement") is made and entered into as of this 11th day of May, 1999 by and
 ---------
among Columbia/HCA Healthcare Corporation, a Delaware corporation
("Columbia/HCA"), LifePoint Hospitals, Inc., a Delaware corporation (together
  ------------
with its successors and permitted assigns, "LifePoint"), and Triad Hospitals,
                                            ---------
Inc., a Delaware corporation (together with its successors and permitted
assigns, "Triad").
          -----

          WHEREAS, Columbia/HCA, LifePoint and Triad have entered into that
certain Distribution Agreement, dated as of May 11, 1999 (the "Distribution
                                                               ------------
Agreement"), pursuant to which (a) Columbia/HCA and its Subsidiaries shall cause
---------
to be consummated certain corporate transactions in order to divide and separate
their existing businesses and assets so that (i) the Columbia/HCA Business shall
be owned, controlled, and operated, directly and indirectly, by Columbia/HCA,
(ii) the America Group Business shall be owned, controlled, and operated,
directly and indirectly, by LifePoint and (iii) the Pacific Group Business shall
be owned, controlled, and operated, directly and indirectly, by Triad, and (b)
Columbia/HCA shall distribute to the holders of Columbia/HCA's outstanding
shares of common stock, the outstanding shares of America common stock and the
outstanding shares of Pacific common stock owned by Columbia/HCA (such
distributions being collectively referred to as the "Distributions"), upon the
                                                     -------------
terms and subject to the conditions set forth in the Distribution Agreement;

          WHEREAS, Columbia/HCA, its Subsidiaries and their respective
predecessors have historically maintained various insurance policies (the

"Policies") for the benefit or protection of one or more of Columbia/HCA and its
---------
Subsidiaries, some of which are professional liability policies purchased from
Health Care Indemnity, Inc. (the "HCI Policies");
                                  ------------

          WHEREAS, in connection with the transactions contemplated by the
Distribution Agreement, Columbia/HCA,  LifePoint and Triad have determined that
it is necessary and desirable to provide for the respective continuing rights
and obligations in respect of the Policies from and after the Distribution Date
and the administration of claims thereunder as well as interim administration by
Columbia/HCA of new policies entered into by LifePoint and Triad on and after
the Distribution Date;

          WHEREAS, under the Distribution Agreement, Columbia/HCA has agreed to
indemnify LifePoint and Triad for losses in excess of any insurance proceeds
with respect to activities prior to the Distribution Date;

          WHEREAS, the parties desire to enter into this Agreement in order to
define the relationship between the parties regarding insurance of their
respective properties and liabilities and the exercise of certain rights,
remedies and options by the respective parties hereto under the Policies; and

<PAGE>

          WHEREAS, pursuant to the Distribution Agreement the parties hereto
have agreed to enter into this Agreement;

          NOW THEREFORE, in consideration of the mutual agreements, provisions,
and covenants contained in this Agreement and the Distribution Agreement, the
parties hereto hereby agree as follows:

          Unless otherwise defined herein or unless the context otherwise
requires, all capitalized terms shall have the meanings (such meanings to be
equally applicable to both the singular and plural forms of the terms defined)
attributed to them in the Distribution Agreement.

          Section 1.  Allocation of Existing Coverages and Liabilities.
                      ------------------------------------------------

          1.01  Claims in Process. Any claims made against insurers under the
                -----------------
Policies prior to the Distribution Date and unpaid as of such date shall be for
the account of the party (i) whose asset after the Distribution Date is the
basis for the claim, or (ii) in the case of a liability claim, which is the
owner after the Distribution Date of the facility at which the activity which is
the subject of the claim occurred or is alleged to have occurred. If the
proceeds of the claim are received by a party other than the party entitled to
receive such proceeds pursuant to this Section 1.01, such receiving party shall
pay over such proceeds to such other party. In respect of claims under Policies
for the account of LifePoint or Triad, in the event that any deductible, co-
insurance or self-insured retention in respect of such claim has not been paid
or accounted for prior to the Distribution Date, or if the Policy under which
the claim was made provides for any aggregate deductible, co-insurance or self-
insured retention or if the claim is not fully covered because the aggregate
policy limits have been exhausted, such amounts shall be paid to such party by
Columbia/HCA pursuant to the indemnification provided for in the Distribution
Agreement.

          1.02  Retroactive Rate Adjustments.  Retroactive adjustments in
                ----------------------------
respect of any Policies for periods ended on or prior to the Distribution Date
shall be paid or received by Columbia/HCA, and LifePoint and Triad shall have no
liability or receive no refund therefor regardless of the reason for the
adjustment.

          1.03  Incurred But Not Reported Claims.  (a) The parties shall do all
                --------------------------------
things necessary to assure that all Policies which provide coverage remain
applicable to LifePoint and Triad and their respective Subsidiaries and assets
after the Distribution Date, to the extent they were applicable prior to the
Distribution Date with respect to losses incurred prior to the Distribution
Date.

          (b)  The parties shall do all commercially reasonable things necessary
to assure continued coverage for incurred but not reported claims and incidents
which have not been filed with insurers which would have been covered under
Policies which provide coverage on a claims made basis had they been made and
reported prior to the Distribution Date including the purchase of tail coverage
by Columbia/HCA with respect to claims made policies if the replacement policies
acquired by LifePoint or Triad do not have retroactive dates which provide
coverage for all occurrences which would have been covered by the Policies had
they remained in effect after the Distribution Date.

                                       2
<PAGE>

          (c)  Indemnity payments under Policies which are on an occurrence
basis in respect of claims made after the Distribution Date arising out of
occurrences prior to the Distribution Date shall be for the account of the party
(i) whose asset after the Distribution Date was the basis for the claim or (ii)
in the case of liability claims, which is the owner after the Distribution Date
of the facility at which the activity which is the subject of the claim occurred
or is alleged to have occurred; provided, however, that, in respect of claims
                                --------  -------
under Policies for the account of LifePoint or Triad, if the Policy under which
the claim was made provides for any deductible, co-insurance or self-insured
retention or if the claim is not fully covered because the policy limits have
been exhausted, such amounts shall be paid to such party by Columbia/HCA
pursuant to the indemnification provided for in the Distribution Agreement.

          Section 2.  Cooperation and Joint Insurance.
                      -------------------------------
          2.01  Cooperation in Acquiring Insurance.  Columbia/HCA, LifePoint and
                ----------------------------------
Triad shall cooperate with each other in the purchase of insurance coverage for
periods commencing after the Distribution Date with the aim of obtaining
appropriate insurance coverage on the best available terms and conditions and at
the most reasonable rates, always taking into account the quality of the
insurers with which coverage is being placed. The parties anticipate that
LifePoint and Triad will purchase continuous coverage under extensions or
renewals of the HCI Policies, or separate policies issued by Health Care
Indemnity, Inc. which provide continuous coverage. Each party shall be entitled
to purchase its own separate coverage in the event it believes that, after a
good faith attempt to obtain appropriate joint coverage (which shall include an
attempt to agree upon allocation of premium on an other than pro rata basis in
                                                             --- ----
the event the insurer views one party as a higher risk than the other), its own
interests dictate that course of action. In situations in which the parties are
required by law to maintain separate coverage or to make changes in existing
joint coverage, they shall cooperate in so doing.

          Columbia/HCA, LifePoint and Triad agree that there are certain
situations in which existing coverage must be retained as a result of state law
or regulation.  In these situations the parties will cooperate to maintain such
coverage and appropriate financial accommodation will be made so that LifePoint
or Triad, as the case may be, will pay or receive value so that it will be in
the same financial position as it would have been had it obtained coverage
independently.  In this regard the current participation of hospitals in the
patient compensation fund in the state of Kansas will be continued in order to
maintain the retroactive date on claims made coverage.  In consideration
therefore, the value of a tail policy will be transferred.  In addition, in
respect of Triad in the state of Texas the hospitals have opted out of the
workers compensation program and will maintain a benefit program in lieu
thereof.  Reserves will be continued on the books of the participating hospitals
in order to permit the program to continue.

          2.02  Joint Liability and Claims.  (a) In the event that a claim by a
                --------------------------
third party is made against two or more of the parties (or a Subsidiary of a
party and another party or a Subsidiary thereof) (a "Joint Claim"), and
                                                     -----------
indemnification under the Distribution Agreement is provided by Columbia/HCA,
Columbia/HCA shall defend the Joint Claim at its expense and the other party or
parties shall cooperate in such defense. In the event that no indemnification is
provided for under the Distribution Agreement and there is no other existing
agreement or indemnification with respect to such Joint Claim, the parties to
the Joint Claim agree to handle

                                       3
<PAGE>

such Joint Claim in accordance with this Section 2.02. Such parties shall
jointly defend such Joint Claim and shall attempt to agree upon the appropriate
allocation of any liability or expenses. In the event that such parties cannot
agree upon an appropriate allocation, the issue shall be referred to arbitration
in accordance with the procedures described in subsection (b) below, but only
after a final determination of liability (through final court judgment,
settlement or otherwise) has been made. None of the parties, nor any Subsidiary
of any of them, shall institute any court proceedings against the other
involving a Joint Claim.

          In the event that any of the parties purchases separate liability
coverage, each of them shall make known to its insurer this Agreement and in
particular the provisions of this Section 2.02.

          (b)  Any and all disputes arising from or in connection with this
Agreement shall be resolved in accordance with the procedures set forth in
Article XI of the Distribution Agreement (including, without limitation,
provisions set forth therein regarding attempts to amicably resolve any dispute
through discussions among members of senior management, consent to jurisdiction
and waiver of jury trial).

          Section 3.  Administrative Services.
                      -----------------------

          3.01  Engagement.  LifePoint and Triad each authorizes Columbia/HCA to
                ----------
perform and provide the technical and administrative service, assistance and
support functions described in Schedule 3.01 attached hereto (the "Services").
                                                                   --------
Columbia/HCA hereby accepts such appointment. Compensation for such services
shall be as provided for in Schedule 3.01.

          3.02  General Description of the Services.  The purpose of this
                -----------------------------------
Agreement is to set forth the terms upon which Columbia/HCA shall provide to
LifePoint and Triad the Services (i) in connection with the Policies and (ii) on
an interim basis in respect of post-Distribution Date insurance, in order to
permit LifePoint and Triad the opportunity to obtain alternative sources of
supply of the Services. In general, the Services shall be consistent with the
comparable services provided by Columbia/HCA with respect to the Policies
immediately prior to the Distribution Date.

          3.03  Performance by Affiliates.  The Parties recognize that the
                -------------------------
Services may include services which, by their nature, are more effectively to be
provided by Affiliates of Columbia/HCA. Subject to the next sentence of this
Section 3.03, Columbia/HCA shall, to the extent required in order for its
Affiliates to provide such Services, cause its Affiliates to provide such
Services hereunder as if such Affiliates were themselves parties hereto. In
connection with the provision of such Services, Columbia/HCA's Affiliates shall
be entitled, as if such Affiliates were themselves parties hereto, to the
benefits of (i) the limitations on liability set forth herein and (ii) the
limitations on the obligation to provide Services set forth herein.

          Section 4.  Amendment of Policies.
                      ---------------------

          So long as LifePoint or Triad is covered by any Policy, Columbia/HCA
will not enter into any material amendment, change or modification of any such
Policy which would materially adversely affect LifePoint's or Triad's rights
under such Policy without the express

                                       4
<PAGE>

prior written consent to such amendment, change or modification by LifePoint or
Triad, unless all reasonably anticipated claims thereunder are covered by the
indemnification under the Distribution Agreement after taking into account the
amendment, change or modification.

          Section 5.  Access to Records and Other Information.
                      ---------------------------------------

          In order to enable it to prosecute any claim or determine coverage
thereunder, either party, at its expense, may at any reasonable time examine or
copy any letter, account, or other documentation or information in the
possession or control of the other party or any affiliate of such party relating
to or connected with any Policy with respect to a policy period during which
such party or an affiliate was covered thereby and relating to prior losses
which are the subject of this Agreement.  The other party shall, at the request
and expense of the requesting party, take reasonable steps to obtain for the
requesting party any information or documents in the possession of any third
party relating to or in connection with the Documents and identified by the
requesting party.

          Section 6.  Successors and Assigns.
                      ----------------------

          This Agreement and all of the provisions hereof shall be binding upon
and inure to the benefit of the parties and their respective successors and
permitted assigns.  Neither party hereto may assign its rights or delegate its
obligations under this Agreement without the prior written consent of the other
party.

          Section 7.  Counterparts.
                      ------------

          This Agreement may be executed in several counterparts, each of which
shall be deemed an original, but such counterparts shall together constitute one
and the same instrument.

          Section 8.  Governing Law.
                      -------------

          This Agreement shall be governed by and construed in accordance with
the laws of the State of Delaware.

          Section 9.  No Impairments of Other Rights.
                      ------------------------------

          Nothing in this Agreement is intended or shall be construed to impair,
diminish or otherwise adversely affect any other rights under the Policies or
otherwise either party may have or may obtain against any person other than the
other party to this Agreement.

          Section 10. Subrogation.
                      -----------

          Each party agrees that the other party shall be subrogated to such
party's rights and remedies under the Documents to the extent of the portion of
any amounts recoverable thereunder determined in accordance with the terms of
this Agreement regarding allocation of liabilities, losses, claims and expenses.
Each party further agrees to cooperate with the other party in connection with
the other party's enforcement of any such rights and remedies and agrees not to
take any actions that would prejudice the exercise of such right of subrogation.

                                       5
<PAGE>

This Section is not intended to result in any reallocation of amounts
recoverable under this Agreement. It is intended to avoid any waiver of
subrogation.

          Section 11. Subsidiaries.
                      ------------

          Each of the parties hereto shall cause to be performed, and hereby
guarantees the performance of, all actions, agreements and obligations set forth
herein to be performed by any Subsidiary of such party which is contemplated to
be a Subsidiary of such party on and after the Distribution Date; provided,
                                                                  --------
however, that this Section 1 shall not apply to any obligation of Health Care
-------
Indemnity, Inc. pursuant to any Policy under which it is an insurer.

          Section 12. No Third Party Beneficiaries.
                      ----------------------------

          This Agreement is solely for the benefit of the parties hereto and
their respective Subsidiaries and Affiliates and should not be deemed to confer
upon third parties any remedy, claim, liability, reimbursement, claim of action
or other right in excess of those existing without reference to this Agreement.

          Section 13. Construction.  In this Agreement,
                      ------------

                         (i)   unless the context otherwise requires, the terms
          "herein," "hereof," "hereto," and "hereunder" refer to this Agreement;
          and

                         (ii)  the headings of the sections and subsections
          hereof and the table of contents hereof are inserted for convenience
          only and do not constitute a part of this Agreement.

          Section 14. Entire Agreement; Amendment.
                      ---------------------------

          This Agreement including the Schedule hereto, which is an integral
part hereof, the Distribution Agreement and the other agreements referred to
herein or therein or entered into in connection herewith or therewith set forth
the entire agreement and understanding of the parties with respect to the
transactions contemplated hereby and supersede all prior agreements,
arrangements and understandings relating to the subject matter hereof.  No
representation, promise, inducement or statement of intention has been made by
either party hereto which is not embodied in this Agreement or such other
agreements, the Schedules or Exhibits or thereto, or the written statements or
other documents delivered pursuant hereto and thereto, and neither party hereto
shall be bound by or liable for any alleged representation, promise, inducement
or statement of intention not so set forth.  This Agreement may be amended or
modified only by a written instrument executed by both parties hereto or by
their successors and permitted assigns.

          Section 15. Waivers.
                      -------

          No failure or delay on the part of any party in exercising any power
or right hereunder shall operate as a waiver thereof, nor shall any single or
partial exercise of any such right or power, or any abandonment or
discontinuance of steps to enforce such a right or power, preclude any other or
further exercise thereof or the exercise of any other right or power. No
modification or waiver of any provision of this Agreement nor consent to any
departure by any

                                       6
<PAGE>

party therefrom shall in any event be effective unless the same shall be in
writing, and then such waiver or consent shall be effective only in the specific
instance and for the purpose for which given.

          Section 16. Confidentiality.
                      ---------------

          Subject to any contrary requirement of law and the right of each party
to enforce its rights hereunder in any legal action, each party shall keep
strictly confidential, and shall cause its employees and agents to keep strictly
confidential, any information of or concerning the other party which it or any
of its agents or employees may acquire pursuant to, or in the course of
performing its obligations under, any provision of this Agreement; provided,
                                                                   --------
however, that such obligation to maintain confidentiality shall not apply to
-------
information which (i) at the time of disclosure was in the public domain, (ii)
after disclosure enters the public domain not as a result of acts by the
receiving party, (iii) was already independently in the possession of the
receiving party at the time of disclosure or (iv) is received by the receiving
party from a third party who did not receive such information from the
disclosing party under an obligation of confidentiality.

          Section 17. Notices.
                      -------

          All notices, consents, requests, instructions, approvals and other
communications hereunder shall be in writing and shall be deemed to have been
duly given, if delivered in person or by courier, telegraphed, telexed or by
facsimile transmission or mailed, by, certified or registered mail, postage
prepaid at the following address (or at such other address provided by one party
to the other in writing):

If to Columbia/HCA:

                    Columbia/HCA Healthcare Corporation
                    One Park Plaza
                    Nashville, Tennessee 37203
                    Telecopy:  (615) 344-2075
                    Attention:  Robert A. Waterman, Esq.
                                Senior Vice President & General Counsel

     with a copy to:

                    James D. Hinton
                    Vice President of Risk and Insurance
                    Columbia/HCA HealthCare Corporation
                    One Park Plaza
                    Nashville, TN 37203

                                       7
<PAGE>

If to LifePoint, to

                    LifePoint Hospitals, Inc.
                    4525 Harding Road
                    Suite 103
                    Nashville, Tennessee 37205
                    Telecopy: (615) 344-6276
                    Attention:  Mr. Scott L. Mercy
                                Chairman and Chief Executive Officer

     with a copy to:

                    LifePoint Hospitals, Inc.
                    4525 Harding Road
                    Suite 103
                    Nashville, Tennessee 37205
                    Telecopy: (615) 344-6272
                    Attention:  William F. Carpenter III, Esq.
                                Senior Vice President and General Counsel

If to Triad, to

                    Triad Hospitals, Inc.
                    13455 Noel Road
                    20th Floor
                    Dallas, Texas 75240
                    Telecopy: (972)663-3945
                    Attention:  Mr. James D. Shelton
                                President and Chief Executive Officer

     with a copy to:

                    Triad Hospitals, Inc.
                    13455 Noel Road
                    20th Floor
                    Dallas, Texas 75240
                    Telecopy: (972)701-9604
                    Attention:  Donald P. Fay, Esq.
                                Executive Vice President
                                and General Counsel

                                       8
<PAGE>

In each case, with a copy to:

                    Dewey Ballantine LLP
                    1301 Avenue of the Americas
                    New York, New York  10019-6092
                    Telecopy: (212) 259-6333
                    Attention:  Morton A. Pierce, Esq.
                                William W. Rosenblatt, Esq.


          Section 18. Legal Enforceability.
                      --------------------

          Any provision of this Agreement which is prohibited or unenforceable
in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent
of such prohibition or unenforceability without invalidating the remaining
provisions hereof.  Any such prohibition or unenforceability in any jurisdiction
shall not invalidate or render unenforceable such provision or remedies
otherwise available to any party hereto.  Without prejudice to any rights or
remedies otherwise available to any party hereto, each party hereto acknowledges
that damages would be an inadequate remedy for any breach of the provisions of
this Agreement and agrees that the obligations of the parties hereunder shall be
specifically enforceable.

          Section 19. Survival of Agreements.
                      ----------------------

          Except as otherwise contemplated by this Agreement, all covenants and
agreements of the parties contained in this Agreement shall survive the
Distribution Date.

                                       9
<PAGE>

          IN WITNESS WHEREOF, the parties have caused this Agreement to be duly
executed as of the day and year first above written.


                         COLUMBIA/HCA HEALTHCARE CORPORATION


                         By:  /s/ Ronald Lee Grubbs, Jr.
                            -------------------------------
                         Name:  Ronald Lee Grubbs, Jr.
                         Title: Vice President of Tax


                         LIFEPOINT HOSPITALS, INC.

                         By:  /s/ William F. Carpenter III
                            -------------------------------
                         Name:  William F. Carpenter III
                         Title: Senior Vice President, General Counsel and
                                 Secretary

                         TRIAD HOSPITALS, INC.

                         By: /s/ Donald P. Fay
                            -------------------------------
                         Name:  Donald P. Fay
                         Title: Executive Vice President, General Counsel and
                                 Secretary

                                       10
<PAGE>

                               Schedule 3.01(c)

                                [To be agreed.]

                                       11