<PAGE>
                                                                    EXHIBIT 10.2

                               THIRD AMENDMENT TO
                     THIRD AMENDED AND RESTATED AGREEMENT OF
               LIMITED PARTNERSHIP OF UNITED DOMINION REALTY, L.P.

     This THIRD AMENDMENT TO THE THIRD AMENDED AND RESTATED AGREEMENT OF LIMITED
PARTNERSHIP OF UNITED DOMINION REALTY, L.P., dated as of June 20, 2003 (this
"Amendment"), is being executed by United Dominion Realty Trust, Inc., a
Maryland corporation (the "Company"), as the general partner of United Dominion
Realty, L.P., a Virginia limited partnership (the "Partnership"), pursuant to
the authority conferred upon the Company by Section 4.02(a) of the Third Amended
and Restated Agreement of Limited Partnership of United Dominion Realty, L.P.,
dated as of December 7, 1998, as amended and/or supplemented from time to time
(the "Agreement"). Capitalized terms used, but not otherwise defined herein,
shall have the respective meanings ascribed thereto in the Agreement.

     WHEREAS, pursuant to Section 4.02(a) of the Agreement, the Company is
authorized to determine the designations, preferences and relative,
participating, optional or other special rights, powers and duties of
Partnership Units.

     NOW, THEREFORE, in consideration of the foregoing, and other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties hereto agree as follows:

     (1)  The Agreement is hereby amended by the addition of a new exhibit,
entitled "Exhibit D," in the form attached hereto, which shall be attached and
made a part of the Agreement.

     (2)  Except as specifically amended hereby, the terms, covenants,
provisions and conditions of the Agreement shall remain unmodified and continue
in full force and effect and, except as amended hereby, all of the terms,
covenants, provisions and conditions of the Agreement are hereby ratified and
confirmed in all respects.

     IN WITNESS WHEREOF, this Amendment has been executed as of the date first
written above.

                                        UNITED DOMINION REALTY TRUST, INC.


                                        By: /s/ Thomas W. Toomey
                                           -------------------------------------
                                           Thomas W. Toomey
                                           Chief Executive Officer and President

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                                    EXHIBIT D

                          PARTNERSHIP UNIT DESIGNATION
                                     OF THE
                   CLASS II OUT-PERFORMANCE PARTNERSHIP SHARES
                         OF UNITED DOMINION REALTY, L.P.

     1.   NUMBER OF UNITS AND DESIGNATION.

     A class of Partnership Units is hereby designated as "Class II
Out-Performance Partnership Shares," and the number of Partnership Units
initially constituting such class shall be one million (1,000,000).

     2.   DEFINITIONS.

     For purposes of this Partnership Unit Designation, the following terms
shall have the meanings indicated in this Section 2. Capitalized terms used and
not otherwise defined herein shall have the meanings assigned thereto in the
Agreement.

     "Change of Control" shall mean the occurrence of any of the following
events:

     (i)   an acquisition of any voting securities of the Company (the "Voting
Securities") by any "person" (as the term "person" is used for purposes of
Section 13(d) or Section 14(d) of the Securities Exchange Act of 1934, as
amended (the "Exchange Act")) immediately after which such person has
"beneficial ownership" (within the meaning of Rule 13d-3 promulgated under the
Exchange Act) ("Beneficial Ownership") of 30% or more of the combined voting
power of the Company's then outstanding Voting Securities; provided, however, in
determining whether a Change in Control has occurred, Voting Securities that are
acquired in a Non-Control Acquisition (as hereinafter defined) shall not
constitute an acquisition that would cause a Change in Control. "Non-Control
Acquisition" shall mean an acquisition by (A) an employee benefit plan (or a
trust forming a part thereof) maintained by (1) the Company or (2) any
corporation, partnership or other person of which a majority of its voting power
or its equity securities or equity interest is owned directly or indirectly by
the Company or in which the Company serves as a general partner or manager (a
"Subsidiary"), (B) the Company or any Subsidiary, or (C) any person in
connection with a Non-Control Transaction (as hereinafter defined);

     (ii)  the individuals who constitute the Board of Directors of the Company
as of May 6, 2003 (the "Incumbent Board") cease for any reason to constitute at
least two-thirds (2/3) of the members of the Board of Directors of the Company;
provided, however, that if the election, or nomination for election by the
Company's stockholders, of any new director was approved by a vote of at least
two-thirds (2/3) of the Incumbent Board, such new director shall be considered
as a member of the Incumbent Board; provided, further, that no individual shall
be considered a member of the Incumbent Board if such individual initially
assumed office as a result of either an actual or threatened "election contest"
(as described in Rule 14a-11 promulgated under the

<PAGE>

Exchange Act) (an "Election Contest") or other actual or threatened solicitation
of proxies or consents by or on behalf of a person other than the Board of
Directors of the Company (a "Proxy Contest") including by reason of any
agreement intended to avoid or settle any Election Contest or Proxy Contest; or

     (iii) approval by stockholders of the Company of: (A) a merger,
consolidation, share exchange or reorganization involving the Company, unless
(1) the stockholders of the Company immediately before such merger,
consolidation, share exchange or reorganization, own, directly or indirectly
immediately following such merger, consolidation, share exchange or
reorganization, at least 60% of the combined voting power of the outstanding
voting securities of the corporation that is the successor in such merger,
consolidation, share exchange or reorganization (the "Surviving Company") in
substantially the same proportion as their ownership of the Voting Securities
immediately before such merger, consolidation, share exchange or reorganization,
(2) the individuals who were members of the Incumbent Board immediately prior to
the execution of the agreement providing for such merger, consolidation, share
exchange or reorganization constitute at least two-thirds (2/3) of the members
of the board of directors of the Surviving Company, and (3) no persons (other
than the Company or any Subsidiary of the Company, any employee benefit plan (or
any trust forming a part thereof) maintained by the Company, the Surviving
Company or any Subsidiary of the Company, or any person who, immediately prior
to such merger, consolidation, share exchange or reorganization had Beneficial
Ownership of 30% or more of the then outstanding Voting Securities has
Beneficial Ownership of 30% or more of the combined voting power of the
Surviving Company's then outstanding voting securities (a transaction described
in clauses (1) through (3) is referred to herein as a "Non-Control
Transaction"); (B) a complete liquidation or dissolution of the Company; or (C)
an agreement for the sale or other disposition of all or substantially all of
the assets of the Company to any person (other than a transfer to a Subsidiary
of the Company).

     Notwithstanding the foregoing, a Change of Control shall not be deemed to
occur solely because any person (a "Subject Person") acquired Beneficial
Ownership of more than the permitted amount of the outstanding Voting Securities
as a result of the acquisition of Voting Securities by the Company that, by
reducing the number of Voting Securities outstanding, increases the proportional
number of shares Beneficially Owned by such Subject Person, provided that if a
Change of Control would occur (but for the operation of this sentence) as a
result of the acquisition of Voting Securities by the Company, and after such
share acquisition by the Company, such Subject Person becomes the Beneficial
Owner of any additional Voting Securities that increases the percentage of the
then outstanding Voting Securities Beneficially Owned by such Subject Person,
then a Change of Control shall occur.

     "Class II Out-Performance Partnership Share" shall mean a Partnership Unit
with the designations, preferences and relative, participating, optional or
other special rights, powers and duties as are set forth in this Exhibit D.

     "Class II Out-Performance Valuation Date" shall mean the earlier to occur
of (i) May 31, 2005, or (ii) the date on which a Change of Control occurs.

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     "Conversion Factor" shall mean the quotient obtained by (a) multiplying 5%
of the Excess Return by the Company's Market Capitalization and (b) dividing the
number obtained in clause (b) by the market value of one REIT Share on the Class
II Out-Performance Valuation Date, as the weighted average price per day of
common stock for the 20 trading days immediately preceding the Class II
Out-Performance Valuation Date

     "Determination Date" shall mean (i) when used with respect to any dividend
or other distribution, the date fixed for the determination of the holders of
the securities entitled to receive such dividend or distribution, or, if a
dividend or distribution is paid or made without fixing such a date, the date of
such dividend or distribution, and (ii) when used with respect to any split,
subdivision, reverse stock split, combination or reclassification of securities,
the date upon which such split, subdivision, reverse stock split, combination or
reclassification becomes effective.

     "Excess Return" shall mean the amount, if any, by which the cumulative
Total Return of REIT Shares over the Measurement Period exceeds the greater of
the cumulative Total Return of the Morgan Stanley REIT Index, which is the peer
group index, or the Minimum Return.

     "Ex-Date" shall mean (i) when used with respect to any dividend or
distribution, the first date on which the securities on which the dividend or
distribution is payable trade regular way on the relevant exchange or in the
relevant market without the right to receive such dividend or distribution, and
(ii) when used with respect to any split, subdivision, reverse stock split,
combination or reclassification of securities, the first date on which the
securities trade regular way on such exchange or in such market to reflect such
split, subdivision, reverse stock split, combination or reclassification
becoming effective.

     "Extraordinary Distribution" shall mean the distribution by the Company, by
dividend or otherwise, to all holders of its REIT Shares of evidences of its
indebtedness or assets (including securities) other than cash.

     "Family Controlled Entity" means, as to any holder of Class II
Out-Performance Shares, (a) any corporation more than 50% of the outstanding
voting stock of which is owned by such holder and such holder's Family Members,
(b) any trust, whether or not revocable, of which such holder and such holder's
Family Members are the sole beneficiaries, (c) any partnership of which such
holder and such holder's Family Members hold partnership interests representing
at least 25% of such partnership's capital and profits and (d) any limited
liability company of which such holder is the manager and in which such holder
and such holder's Family Members hold membership interests representing at least
25% of such limited liability company's capital and profits.

     "Family Members" means, as to a Person that is an individual, such Person's
spouse, ancestors, descendants (whether by blood or by adoption), brothers,
sisters and inter vivos or testamentary trusts of which only such Person and his
spouse, ancestors, descendants (whether by blood or by adoption), brothers and
sisters are beneficiaries.

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     "First Amendment" means the First Amendment to the Agreement, dated as of
June 1, 2001.

     "Industry Total Return" shall mean the Total Return of the securities
included in the Industry Peer Group Index for the Measurement Period, with such
average determined in a manner consistent with the manner in which such index is
calculated; provided, however, that if such Industry Total Return would be less
than zero without giving effect to the reinvestment of dividends, then the
"Industry Total Return" shall be equal to zero.

     "Industry Peer Group Index" shall mean the Morgan Stanley REIT Index.

     "Initial Holder" shall mean UDR Out-Performance II, LLC, a Maryland limited
liability company.

     "Measurement Period" shall mean the 24 month period beginning June 1, 2003
to but excluding the Class II Out-Performance Valuation Date.

     "Minimum Return" shall mean a 22% Total Return (compounded annually) or 11%
annualized as of the Class II Out-Performance Valuation Date or, if the Class II
Out-Performance Valuation Date is not May 31, 2005, 11% (compounded annually)
per annum from June 1, 2003.

     "Morgan Stanley REIT Index" shall mean the Morgan Stanley REIT Index quoted
on the American Stock Exchange under the symbol "RMS".

     "Partnership" shall mean United Dominion Realty, L.P., a Virginia limited
partnership.

     "Total Return" shall mean, for any security or index and for any period,
the cumulative total return for such security or index over such period, as
measured by the sum of (a) the cumulative amount of dividends paid in respect of
such security or index for such period (assuming that all cash dividends are
reinvested in such security as of the payment date for such dividend based on
the security price on the dividend payment date), and (b) an amount equal to (x)
the security price or index value at the end of such period, minus (y) the
security price or index value at the beginning of the measurement period.

     "UDR Market Capitalization" shall mean the average number of REIT Shares
outstanding over the Measurement Period (including, for this purpose, REIT
Shares, Partnership Units, outstanding options and convertible securities, but
not including Class II Out-Performance Partnership Shares) multiplied by the
daily closing price of the REIT Shares.

     "UDR Total Return" shall mean the Total Return of the REIT Shares for the
Measurement Period.

<PAGE>

     3.   FORFEITURE.

     If, on the Class II Out-Performance Valuation Date, there is no Excess
Return, then, from and after such date, each Class II Out-Performance
Partnership Share shall, without any action on the part of the Partnership, the
Company or the holder thereof, be automatically forfeited and be no longer
outstanding.

     4.   DISTRIBUTIONS.

     Subject to Section 5.06 of the Agreement, on and after the Class II
Out-Performance Valuation Date, the holders of Class II Out-Performance
Partnership Shares not forfeited under Section 3 shall be entitled to receive
distributions at the same time and in the same amount that would be received on
the number of Partnership Units held by Outside Partners (assuming such
Partnership Units were originally issued on the Class II Out-Performance
Valuation Date) that is obtained by multiplying the number of Class II
Out-Performance Partnership Shares by the Conversion Factor.

     5.   ALLOCATIONS.

          (a)  From and after the Class II Out-Performance Valuation Date,
Profits and Losses shall be allocated to each of the holders of Class II
Out-Performance Partnership Shares not forfeited under Section 3 at the same
time and in the same amount that would be allocated on the number of Partnership
Units held by Outside Partners (assuming such Partnership Units were originally
issued on the Class II Out-Performance Valuation Date) that is obtained by
multiplying the number of Class II Out-Performance Partnership Shares by the
Conversion Factor.

          (b)  In the event that the Partnership disposes of all or
substantially all of its assets in a transaction that will lead to a liquidation
of the Partnership pursuant to Article II of the Agreement, then,
notwithstanding Section 5.06 of the Agreement, each holder of Class II
Out-Performance Partnership Shares not forfeited under Section 3 shall be, to
the extent possible, specially allocated items of Partnership income and gain in
an amount sufficient to cause the Capital Account of such holder to be equal to
that of an Outside Partner that holds Partnership Units equal to the number of
Class II Out-Performance Partnership Shares held by such holder multiplied by
the Conversion Factor. Amounts allocated pursuant to this Section 5(b) and/or
Section 5(b) of the First Amendment shall be excluded from "Profits" and
"Losses" otherwise determined under the Agreement.

     6.   EXCHANGE.

     If the Class II Out-Performance Partnership Shares have not been forfeited
under Section 3 and the Class II Out-Performance Partnership Shares have been
transferred by the Initial Holder in accordance with Section 8, the transferee
and subsequent transferees of the Class II Out-Performance Partnership Shares
may exchange from time to time some or all of the Class II Out-Performance
Partnership Shares for a number Partnership Units equal to the Class II
Out-Performance Partnership Shares multiplied by the Conversion Factor.

<PAGE>

     7.   REDEMPTION UPON CHANGE OF CONTROL.

     Upon the occurrence of a Change of Control, and subject to the applicable
requirements of Federal securities laws and any securities exchange or quotation
system rules or regulations, each holder of Class II Out-Performance Partnership
Shares shall have the redemption rights of Limited Partners set forth in Section
8.05 of the Agreement with respect to a number of Partnership Units equal to the
number of Class II Out-Performance Partnership Shares multiplied by the
Conversion Factor and the 40-month transfer limitation period applicable to the
Class II Out-Performance Partnership Shares shall be deemed to have passed.

     8.   RESTRICTIONS ON OWNERSHIP AND TRANSFER.

     The restrictions on Transfer set forth in Article IX of the Agreement shall
not apply to Transfers of Class II Out-Performance Partnership Shares. Prior to
the Class II Out-Performance Valuation Date, the Class II Out-Performance
Partnership Shares shall be owned and held solely by the Initial Holder. On or
after the later of the Class II Out-Performance Valuation Date and the twenty
four (24) month period from the date the Class II Out-Performance Partnership
Shares are issued the Class II Out-Performance Partnership Shares may be
Transferred (i) by the Initial Holder to (a) any Person who is a member (a
"Member") of the Initial Holder immediately prior to such transfer, (b) a Family
Member of a Member, (c) a Family Controlled Entity of a Member, (d) any Person
with respect to whom the Member constitutes a Family Controlled Entity, (e) upon
the death of a Member, by will or by the laws of descent and distribution to any
Family Member or Family Controlled Entity, and (ii) by any other Person to (a) a
Family Member of a such Person, (b) a Family Controlled Entity of such Person,
(c) any other Person with respect to whom such Person constitutes a Family
Controlled Entity, (d) upon the death of such Person, by will or by the laws of
descent and distribution to any Family Member or Family Controlled Entity;
provided, however, that, until May 31, 2005, the Class II Out-Performance
Partnership Shares may not be Transferred by the Initial Holder without the
approval of the managers of the Initial Holder.

     9.   ADJUSTMENTS.

          (a)  In the event of any Extraordinary Distribution occurring on or
after May 6, 2003, for purposes of determining the Value of a REIT Share or the
UDR Total Return, each price of a REIT Share determined as of a date on or after
the Ex-Date for such Extraordinary Distribution shall be adjusted by multiplying
such price by a fraction (i) the numerator of which shall be the price of a REIT
Share on the date immediately prior to such Ex-Date, and (ii) the denominator of
which shall be (A) the price of a REIT Share on the date immediately prior to
such Ex-Date, minus (B) the fair market value on the date fixed for such
determination of the portion of the evidences of indebtedness or assets so
distributed applicable to one REIT Share (as determined by the Company, whose
determination shall be conclusive); provided further, that such amount shall be
so adjusted for each such Extraordinary Distribution occurring on or after May
6, 2003.

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          (b)  In the event that, on or after May 6, 2003, the Company (i)
declares or pays a dividend on its outstanding REIT Shares in REIT Shares or
makes a distribution to all holders of its outstanding REIT Shares in REIT
Shares, (ii) splits or subdivides its outstanding REIT Shares, (iii) effects a
reverse stock split or otherwise combines its outstanding REIT Shares into a
smaller number of REIT Shares, or (iv) otherwise reclassifies its outstanding
REIT Shares, then, for purposes of determining the Value of a REIT Share or the
UDR Total Return, each price of a REIT Share determined as of a date on or after
the Ex-Date for such transaction shall be adjusted by multiplying such price by
a fraction (x) the numerator of which shall be the number of REIT Shares issued
and outstanding on the Determination Date for such dividend, distribution,
split, subdivision, reverse stock split, combination or reclassification
(assuming for such purposes that such dividend, distribution, split,
subdivision, reverse split or combination has occurred as of such time) and (y)
the denominator of which shall be the actual number of REIT Shares (determined
without the above assumption) issued and outstanding on the Determination Date
for such dividend, distribution, split, subdivision, reverse stock split.
combination or reclassification.

          (c)  The Company shall have authority to appropriately adjust the UDR
Market Capitalization, the UDR Total Return or the Value of a REIT Share if any
other transaction or circumstance occurs or arises that without such adjustment
would have an inequitable result.

     10.  GENERAL.

     The ownership of Class II Out-Performance Partnership Shares may (but need
not, in the sole and absolute discretion of the Company) be evidenced by one or
more certificates. The Company shall amend Exhibit A to the Agreement from time
to time to the extent necessary to reflect accurately the issuance of, and
subsequent conversion, redemption, or any other event having an effect on the
ownership of Class II Out-Performance Partnership Shares.

<PAGE>

     IN WITNESS WHEREOF, ASR, Heritage SGP and UDR have caused this First
Amendment to be signed by their respective officers thereunto duly authorized,
all as of the date first written above.

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                                        ASR INVESTMENTS CORPORATION


                                        By:   /s/ [illegible]
                                             -----------------------------------
                                        Its: President


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                                        HERITAGE SGP CORPORATION


                                        By:   /s/ [illegible]
                                             -----------------------------------
                                        Its: President


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                                        UNITED DOMINION REALTY TRUST, INC.


                                        By:   /s/ Kathryn Surface
                                             -----------------------------------
                                        Its: Senior Vice President


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