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                                                                    EXHIBIT 10.4
                                                                  CONFORMED COPY


                               FOUNDERS AGREEMENT
                                  (Old United)

         This Founders Agreement (Old United) (this "AGREEMENT") is entered into
as of January 30, 2002 among Albert M. Carollo, Curtis Rochelle, Gene W.
Schneider and Mark L. Schneider (each a "FOUNDER" and collectively the
"FOUNDERS").

                                   BACKGROUND

         The Founders are among the founding stockholders of UnitedGlobalCom,
Inc., a Delaware corporation to be renamed UGC Holdings, Inc. ("OLD UNITED").
Each Founder holds shares of Class B Common Stock, par value $0.01 per share
("OLD UNITED CLASS B COMMON"), of Old United, either directly or through
affiliates of such Founder who are parties to a Founders' Agreement, dated as of
September 30, 1999 (the "1999 FOUNDERS AGREEMENT"), among the Founders and
certain other holders of Old United Class B Common. An individual Founder and
his Related Parties are referred to as a "FOUNDER GROUP."

         The Founders acquired an aggregate of 1,500 shares of Series E
Preferred Stock of Old United pursuant to Subscription Agreements with Old
United dated as of January 30, 2002. Pursuant to the Amended and Restated
Agreement and Plan of Restructuring and Merger, dated as of December 31, 2001
(the "MERGER AGREEMENT"), among Old United, New UnitedGlobalCom, Inc., a
Delaware corporation to be renamed UnitedGlobalCom, Inc. ("NEW UNITED"), Liberty
Media Corporation, Liberty Media International, Inc. and the Founders, et al.,
such shares of Series E Preferred Stock will be converted into the right to
receive 1,500 shares of Class A Common Stock, par value $0.01 per share, of Old
United (the "OLD UNITED CLASS A COMMON"). Pursuant to the Restated Certificate
of Incorporation of Old UGC to be filed pursuant to the Merger Agreement (the
"RESTATED CERTIFICATE"), the Founders as holders of the Old United Class A
Common, will be entitled to elect one-half of the members of the board of
directors of Old United, such half to consist of four persons.

         Each share of Old United Class A Common will automatically convert into
one share of Class C Common Stock, par value $0.01 per share (the "OLD UNITED
CLASS C COMMON"), of Old United upon the occurrence of certain events set forth
in the Restated Certificate. At the closing of the transactions contemplated by
the Merger Agreement (the "CLOSING"), each Founder will execute and deliver an
Exchange Agreement with New United pursuant to which shares of Old United Class
C Common may be exchanged for shares of Class A Common Stock, par value $0.01
per share, of New United, all at the election of such Founder.

         The Founders desire to set forth the manner of selecting persons who
will be elected as members of the board of directors of Old United by the
Founders as holders of Old United Class A Common, to set forth their agreement
as to the voting of shares of Old United Class A Common on other matters and to
set forth certain restrictions on the transfer of shares of Old United Class A
Common.

                                    AGREEMENT

         Section 1. BOARD NOMINATIONS. The Founders agree that until such time
as no shares of Old United Class A Common remain outstanding, nominees to the
board of directors of Old

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United will be selected as follows, and that the Founders and their Related
Parties will take such actions as may be necessary to elect such nominees as
members of the board of directors of Old United.

         (a) Each of the Founders shall be nominated to the board of directors
as long as he wishes to be nominated, provided his Founder Group owns at least
30 percent of the New United Class B Common received for shares of Old United
Class B Common owned by his Founder Group on the date of this Agreement. If he
decides not to be nominated, he may designate a nominee so long as the nominee
is reasonably qualified to serve as a director of Old United.

         (b) If a Founder dies or becomes incapacitated or if he is no longer
entitled to be nominated to the board of directors or to designate a nominee
pursuant to Section 1(a), the remaining Founders (the "REMAINING FOUNDERS") may
select a nominee in lieu of such Founder or designee so long as the nominee is
reasonably qualified to serve as a director of the Company. In the absence of
unanimous agreement among the remaining Founders, such nominee shall be selected
by the Remaining Founder(s) whose Founder Group(s) hold a majority of the New
United Class B Common then held by all Remaining Founders and their Related
Parties.

         Section 2. STOCKHOLDER ACTION ON OTHER MATTERS. The Founders agree that
until such time as no shares of Old United Class A Common remain outstanding,
the Founders shall vote all shares of Old United Class A Common, other than in
the election of directors (which shall be governed by Section 1), and shall take
all actions as a stockholder of Old United, as the Remaining Founders shall
agree. In the absence of unanimous agreement among the Remaining Founders, such
voting and actions shall be taken as directed by the Remaining Founder(s) whose
Founder Group(s) hold a majority of New United Class B Common then held by all
Remaining Founders and their Related Parties.

         Section 3. PROHIBITIONS ON TRANSFER.

         (a) No Founder may sell, pledge, hypothecate, transfer, assign or
otherwise dispose of, directly or indirectly (each a "TRANSFER"), any shares of
Old United Class A Common to any other Person (including through the
relinquishment of control of any person that holds shares of Old United Class A
Common) other than to a Related Party of such Founder, provided that none of the
following shall constitute a Transfer: (i) the conversion of shares of Old
United Class A Common into shares of Old United Class C Common, or (ii) a
transfer in connection with any merger, consolidation, statutory share exchange
or similar transaction involving Old United.

         (b) Any Founder may Transfer shares of Old United Class A Common to a
Related Party of such Founder if the Related Party undertakes in writing to be
subject to each of the terms of this Agreement as though it were a Founder
hereunder.

         (c) Any purported Transfer of shares of Old United Class A Common in
violation of this Section 3 shall be void and ineffective as against both the
transferring Founder or Related Party and the proposed transferee.

         Section 4. TERMINATION. This Agreement shall terminate as to any
Founder and his Related Parties when such Founder and his Related Parties no
longer own any Old United Class


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A Common. This Agreement shall terminate in its entirely upon the occurrence of
a Class B Event (as defined in the Restated Certificate).

         Section 5. LEGEND. Each Founder shall have a legend substantially
similar to the following effect placed on each certificate for shares of Old
United Class A Common issued to such Founder or to any Related Party of such
Founder:

                  "The securities represented by this certificate are subject to
                  a Founders Agreement (Old United), dated as of January 30,
                  2002, copies of which are available from UGC Holdings, Inc.
                  upon request, and any sale, pledge, hypothecation, transfer,
                  assignment or other disposition of such securities is subject
                  to the provisions of such Founders Agreement."

The Founders shall deliver to Old United a copy of this Agreement and any
amendments thereto so that Old United can comply with requests to make copies of
this agreement available as contemplated by such legend.

         Section 6. REMEDIES. Each of the parties acknowledges and agrees that
in the event of any breach of this Agreement, the nonbreaching party would be
irreparably harmed and could not be made whole by monetary damages. Accordingly,
the parties to this Agreement, in addition to any other remedy to which they may
be entitled hereunder or at law or in equity, shall be entitled to compel
specific performance of this Agreement.

         Section 7. NOTICES. All notices, requests, demands and other
communications required or permitted under this Agreement shall be in writing,
shall be deemed to have been duly given when delivered personally or, sent by
telecopy, or recognized service providing for guaranteed delivery, addressed to
a Founder at the address for such Founder set forth on Exhibit A hereto. All
notices, requests, demands, waivers and communications shall be deemed to have
been given on the date of delivery or on the first business day after overnight
delivery was guaranteed by a recognized delivery service, except that any change
of address shall be effective only upon actual receipt. Written notice given by
telecopy shall be deemed effective when confirmation is received by the sending
party.

         Section 8. ENTIRE AGREEMENT. This Agreement, together with the Merger
Agreement and the other Transaction Documents (as defined in the Merger
Agreement), contains all the terms and conditions agreed upon by the parties
hereto, and no other agreements, oral or otherwise, regarding the subject matter
hereof shall have any effect unless in writing and executed by the parties after
the date of this Agreement. This Agreement supersedes in its entirety the 1999
Founders Agreement.

         Section 9. APPLICABLE LAW, JURISDICTION. This Agreement shall be
governed by Colorado law without regard to conflicts of law rules. The parties
hereby irrevocably submit to the jurisdiction of any Colorado State or United
States Federal court sitting in Colorado, and only a State or Federal Court
sitting in Colorado will have any jurisdiction over any action or proceeding
arising out of or relating to this Agreement or any agreement contemplated
hereby,


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and the undersigned hereby irrevocably agree that all claims in respect of such
action or proceeding shall be heard and determined in such State or Federal
court.

         Section 10. HEADINGS. The headings in this Agreement are for
convenience only and are not to be considered in interpreting this Agreement.

         Section 11. COUNTERPART EXECUTION. This Agreement may be executed in
any number of counterparts, each of which shall be deemed an original but all of
which will constitute a single agreement.

         Section 12. PARTIES IN INTEREST. Nothing in this Agreement, express or
implied, is intended to confer upon any person other than the Founder and their
Related Parties, any benefits, rights or remedies. Neither this Agreement nor
the rights or obligations of any party may be assigned or delegated (other than
to a Related Party that becomes a party hereto in accordance with the terms
hereof) by operation of law or otherwise without the prior written consent of
all other parties hereto.

         Section 13. SEVERABILITY. The invalidity or unenforceability of any
provision of this Agreement in any application shall not affect the validity or
enforceability of such provision in any other application or the validity or
enforceability of any other provision.

         Section 14. WAIVERS AND AMENDMENTS. No waiver of any provision of this
Agreement shall be deemed a further or continuing waiver of that provision or a
waiver of any other provision of this Agreement. This Agreement may not be
amended except in a writing signed by the remaining Founders.

         Section 15. INTERPRETATION. As used herein, except as otherwise
indicated herein or as the context may otherwise require, the words "include,"
"includes" and "including" are deemed to be followed by "without limitation"
whether or not they are in fact followed by such words or words of like import;
the words "hereof," "herein," "hereunder" and comparable terms refer to the
entirety of this Agreement, and not to any particular section or other
subdivision hereof; any pronoun shall include the corresponding masculine,
feminine and neuter forms; the singular includes the plural and vice versa;
references to "Section" or another subdivision are to a section or subdivision
hereof; and all references to "the date hereof," "the date of this Agreement" or
similar terms (but excluding references to the date of execution hereof) refer
to the date first above written, notwithstanding that the parties may have
executed this Agreement on a later date. Any reference herein to a "day" or
number of "days" (without the explicit qualification of "business") shall be
deemed to refer to a calendar day or number of calendar days. If any action or
notice is to be taken or given on or by a particular calendar day, and such
calendar day is not a business day, then such action or notice may be taken or
given on the next succeeding business day.


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         Executed as of the date first set forth above.



                                            /s/ GENE W. SCHNEIDER
                                            -----------------------------------
                                            Gene W. Schneider, Founder





                                            /s/ MARK L. SCHNEIDER
                                            -----------------------------------
                                            Mark L. Schneider, Founder




                                            /s/ CURTIS ROCHELLE
                                            -----------------------------------
                                            Curtis Rochelle, Founder




                                            /s/ ALBERT M. CAROLLO
                                            -----------------------------------
                                            Albert M. Carollo, Founder

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                                    EXHIBIT A

<Table>
<Caption>
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FOUNDER                                                      ADDRESS
---------------------------------------------------------------------------------------------------------
<S>                                                          <C>
Gene W. Schneider                                            c/o UnitedGlobalCom, Inc.
                                                             4643 South Ulster Street, #1300
                                                             Denver, Colorado 80237
                                                             Attention:  Gene W. Schneider
                                                             Telephone: (303) 770-4001
                                                             Telecopier: (303) 220-3117
---------------------------------------------------------------------------------------------------------
Mark L. Schneider                                            c/o UnitedGlobalCom, Inc.
                                                             4643 South Ulster Street, #1300
                                                             Denver, Colorado 80237
                                                             Attention:  Mark L. Schneider
                                                             Telephone: (303) 770-4001
                                                             Telecopier: (303) 220-3117
---------------------------------------------------------------------------------------------------------
Curtis Rochelle                                              c/o UnitedGlobalCom, Inc.
                                                             4643 South Ulster Street, #1300
                                                             Denver, Colorado 80237
                                                             Attention:  Curtis W. Rochelle
                                                             Telephone: (303) 770-4001
                                                             Telecopier: (303) 220-3117
---------------------------------------------------------------------------------------------------------
Albert M. Carollo                                            c/o UnitedGlobalCom, Inc.
                                                             4643 South Ulster Street, #1300
                                                             Denver, Colorado 80237
                                                             Attention: Albert M. Carollo
                                                             Telephone: (303) 770-4001
                                                             Telecopier: (303) 220-3117
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