Document:

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                                                                     EXHIBIT 4.4

        THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
        1933, AS AMENDED, OR ANY STATE SECURITIES LAWS. THEY HAVE BEEN ACQUIRED
        SOLELY FOR INVESTMENT AND NOT WITH A VIEW TO, OR IN CONNECTION WITH, THE
        SALE OR DISTRIBUTION THEREOF. THEY MAY NOT BE SOLD, OFFERED FOR SALE,
        PLEDGED, HYPOTHECATED OR OTHERWISE DISTRIBUTED IN THE ABSENCE OF AN
        EFFECTIVE REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF
        COUNSEL, SATISFACTORY IN FORM AND SUBSTANCE TO THE COMPANY THAT SUCH
        REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OF 1933, AS
        AMENDED AND ANY APPLICABLE STATE SECURITIES LAWS.

NO. B-3                             WARRANT                     FEBRUARY 8, 1999

 TO PURCHASE 166,666.6 SHARES OF SERIES B CUMULATIVE CONVERTIBLE PREFERRED STOCK
                    OF UNIVERSAL ACCESS, INC. (THE "COMPANY")

        1. Number of Shares: Exercise Price: Term. This certifies that ICG
Capital Group, Inc. or its permitted assigns (the "Holder") is entitled, upon
the terms and subject to the conditions hereinafter set forth, at any time after
the date hereof and at or prior to 11:59 p.m. Central Time, on February 8, 2004
(the "Expiration Time"), but not thereafter, to acquire from the Company, in
whole or in part, from time to time, up to 166,666.6 fully paid and
nonassessable shares (the "Shares") of Series B Convertible Preferred Stock, par
value $3.00 per share of the Company ("Series B Preferred Stock"), at a purchase
price of $0.01 (1cents) per Share (the "Exercise Price"). The number of Shares,
type of security for which this Warrant is exercisable and Exercise Price are
subject to adjustment as provided herein, and all references to "Series B
Preferred Stock" and "Exercise Price" herein shall be deemed to include any such
adjustment or series of adjustments.

        2. Exercise of Warrant.

               (a) In general, the purchase rights represented by this Warrant
are exercisable by the Holder, in whole or in part, at any time, or from time to
time, prior to the Expiration Time, by the surrender of this Warrant and the
Notice of Exercise annexed hereto, all duly completed and executed on behalf of
the Holder, at the office of the Company in Chicago, Illinois, (or such other
office or agency of the Company as it may designate by notice in writing to the
Holder at the address of the Holder appearing on the books of the Company), and
upon payment of the Exercise Price for the Shares thereby purchased (by cash,
certified or cashier's check, or wire transfer payable to the order of the
Company, at the time of exercise in an amount equal to the purchase price of the
Shares thereby purchased or by net issue exercise pursuant to Section 2(b)
hereof). Thereupon the Holder shall be entitled to receive from the Company a
stock certificate in proper form representing the number of Shares so purchased,
and a new Warrant in substantially identical form and dated as of such exercise
for the purchase of that number of Shares equal to the difference, if any,
between the number of Shares subject hereto and the number of Shares as to which
this Warrant is so exercised.

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               (b) Net Issue Exercise. Notwithstanding any provisions in this
Warrant to the contrary, if the fair market value of one share of Series B
Preferred Stock (the "Fair Market Value") is greater than the Exercise Price (at
the date of calculation as set forth below), in lieu of exercising this Warrant
by paying the Exercise Price in cash, the Holder may elect to receive shares
equal to the value (as determined below) of this Warrant (or the portion of the
Warrant being exercised and canceled) by surrender of this Warrant at the
principal office of the Company together with the properly endorsed Notice of
Exercise and notice of such election, in which event the Company shall issue to
the Holder a number of shares of Series B Preferred Stock computed using the
following formula:

               X = Y (A-B)
                   -------
                      A

        Where         X =   the number of shares of Series B Preferred Stock to
                            be issued to the Holder

                      Y =   the number of shares of Series B Preferred Stock
                            purchasable under the Warrant, or if only a portion
                            of the Warrant is being exercised, the portion of
                            the Warrant being exercised and canceled (at the
                            date of such calculation)

                      A =   the Fair Market Value

                      B =   the Exercise Price

For purposes of the above calculation, the Fair Market Value shall be determined
by the Company's Board of Directors in good faith; provided, however, that where
there exists a public market for the Company's common shares, no par value per
share (the "Common Shares") at the time of such exercise, the Fair Market Value
shall be the product of (i) the average of the closing bid and asked prices of
the Common Shares quoted in the Over-The-Counter Market Summary or the last
reported sale price of the Common Shares or the closing price quoted on the
NASDAQ National Market or on any exchange on which the Common Shares are listed,
whichever is applicable, as published in the Central Edition of The Wall Street
Journal for the five (5) trading days prior to the date of determination of Fair
Market Value and (ii) the number of Common Shares into which each share of
Series B Preferred Stock is convertible at the time of such exercise.
Notwithstanding the foregoing, if the Warrant is exercised in connection with
the Company's initial public offering of Common Shares, the Fair Market Value
shall be the product of (i) the per share offering price to the public of the
Company's initial public offering, and (ii) the number of Common Shares into
which each share of Series B Preferred Stock is convertible at the time of such
exercise.

        3. Issuance of Shares. Certificates for Shares purchased hereunder shall
be delivered to the Holder within a reasonable time after the date on which this
Warrant shall have been exercised in accordance with the terms hereof. All
Shares that may be issued upon the exercise of this Warrant

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shall, upon such exercise, be duly and validly authorized and issued, fully paid
and nonassessable and free from all taxes, liens and charges in respect of the
issuance thereof (other than liens or charges created by or imposed upon the
Holder or taxes in respect of any transfer occurring contemporaneously or
otherwise specified herein). The Company agrees that the Shares so issued shall
be and shall for all purposes be deemed to have been issued to the Holder as the
record owner of such Shares as of the close of business on the date on which
this Warrant shall have been exercised or converted in accordance with the terms
hereof.

        4. No Fractional Shares or Scrip. No fractional Shares or scrip
representing fractional Shares shall be issued upon the exercise of this
Warrant. In lieu of any fractional Share to which the Holder would otherwise be
entitled, the Holder shall be entitled, at its option, to receive either (i) a
cash payment equal to the excess of fair market value for such fractional Share
above the Exercise Price for such fractional share (as determined in good faith
by the Company) or (ii) a whole Share if the Holder tenders the Exercise Price
for one whole share.

        5. No Rights as Shareholders. This Warrant does not entitle the Holder
to any voting rights or other rights as a shareholder of the Company prior to
the exercise hereof.

        6. Charges, Taxes and Expenses. Certificates for Shares issued upon
exercise of this Warrant shall be issued in the name of the Holder. Issuance of
certificates for Shares upon the exercise of this Warrant shall be made without
charge to the Holder for any issue or transfer tax or other incidental expense
in respect of the issuance of such certificates, all of which taxes and expenses
shall be paid by the Company.

        7. Exchange and Registry of Warrant. This Warrant is exchangeable, upon
the surrender hereof by the registered Holder at the office or agency of the
Company referenced in Section 2 above, for a new Warrant on substantially
identical form and dated as of such exchange. The Company shall maintain at the
office or agency referenced in Section 2 above, a registry showing the name and
address of the registered Holder of this Warrant. This Warrant may be
surrendered for exchange or exercise, in accordance with its terms, at the
office of the Company, and the Company shall be entitled to rely in all
respects, prior to written notice to the contrary, upon such registry.

        8. Loss, Theft, Destruction or Mutilation of Warrant. Upon receipt by
the Company of evidence reasonably satisfactory to it of the loss, theft,
destruction or mutilation of this Warrant, and in the case of loss, theft or
destruction, of indemnity or security reasonably satisfactory to it, and upon
reimbursement to the Company of all reasonable expenses incidental thereto, and
upon surrender and cancellation of this Warrant, if mutilated, the Company will
make and deliver a new Warrant of like tenor and dated as of such cancellation
and reissuance, in lieu of this Warrant.

        9. Saturdays, Sundays, Holidays, etc. If the last or appointed day for
the taking of any action or the expiration of any right required or granted
herein shall be a Saturday or a Sunday or shall be a legal holiday, then such
action may be taken or such right may be exercised on the next succeeding day
not a Saturday or a Sunday or a legal holiday.

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<PAGE>   4

        10. Adjustments of Rights. The purchase price per Share and the number
of Shares purchasable hereunder are subject to adjustment from time to time as
follows:

               (a) Merger or Consolidation. If at any time there shall be a
merger or a consolidation of the Company with or into another corporation when
the Company is not the surviving corporation, then, as a condition of such
merger or consolidation, lawful provision shall be made so that the Holder shall
thereafter be entitled to receive upon exercise of this Warrant, during the
period specified herein and upon payment of the aggregate Exercise Price then in
effect, the number of shares of stock or other securities or property (including
cash) of the successor corporation resulting from such merger or consolidation,
to which the holder of the stock deliverable upon exercise of this Warrant would
have been entitled in such merger or consolidation if this Warrant had been
exercised immediately before such merger or consolidation. In any such case,
appropriate adjustment shall be made in the application of the provisions of
this Warrant with respect to the rights and interests of the Holder after the
merger or consolidation. This provision shall apply to successive mergers or
consolidations.

               (b) Reclassification, Recapitalization, etc. If the Company at
any time shall, by subdivision, combination or reclassification of securities,
recapitalization, automatic conversion, or other similar event affecting the
number or character of outstanding Shares, or otherwise, change any of the
securities as to which purchase rights under this Warrant exist into the same or
a different number of securities of any other class or classes, this Warrant
shall thereafter represent the right to acquire such number and kind of
securities as would have been issuable as the result of such change with respect
to the securities that were subject to the purchase rights under this Warrant
immediately prior to such subdivision, combination, reclassification or other
change.

               (c) Split, Subdivision or Combination of Shares. If the Company
at any time while this Warrant remains outstanding and unexpired shall split,
subdivide or combine the securities as to which purchase rights under this
Warrant exist, the Exercise Price shall be proportionately decreased in the case
of a split or subdivision or proportionately increased in the case of a
combination.

               (d) Stock Dividends. If the Company at any time while this
Warrant is outstanding and unexpired shall pay a dividend with respect to Series
B Preferred Stock payable solely in shares of the Company's equity securities,
then the Exercise Price shall be adjusted, from and after the date of
determination of the shareholders entitled to receive such dividend, to that
price determined by multiplying the Exercise Price in effect immediately prior
to such date of determination by a fraction (i) the numerator of which shall be
the total number of Common Shares outstanding immediately prior to such
dividend, and (ii) the denominator of which shall be the total number of Common
Shares outstanding immediately after such dividend.

        The number of Common Shares at any time outstanding (A) shall include,
in addition to outstanding Common Shares, the number of Common Shares into which
the Series B Preferred Stock, the Series A Cumulative Convertible Preferred
Stock, the Series C Convertible Preferred Stock, or

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any of the Company's other equity securities, indebtedness or other securities
are convertible; (B) shall include the number of Common Shares into which any of
the Company's vested options or warrants (including warrants exercisable for
equity securities or indebtedness convertible into Common Shares) are then
convertible; and (B) shall not include treasury shares. This paragraph shall
apply only if and to the extent that, at the time of such event, this Warrant is
then exercisable for Series B Preferred Stock.

               (e) Adjustment of Number of Shares. Upon each adjustment in the
Exercise Price pursuant to 10(c) or 10(d) hereof, the number of Shares
purchasable hereunder shall be adjusted, to the nearest whole Share, to the
product obtained by multiplying the number of Shares purchasable immediately
prior to such adjustment in the Exercise Price by a fraction (i) the numerator
of which shall be the Exercise Price immediately prior to such adjustment, and
(ii) the denominator of which shall be the Exercise Price immediately after such
adjustment.

               (f) Dividends. If the Company declares or pays a dividend or
other distribution upon the Series B Preferred Stock other than a stock dividend
payable solely in shares of the Company's equity securities (a "Dividend"), then
the Company shall pay to the Holder at the time of payment thereof the Dividend
which would have been paid to such Holder if such Holder had held the maximum
number of Shares acquirable upon complete exercise of the outstanding portion of
this Warrant immediately prior to the date on which a record is taken for such
Dividend, or, if no record is taken, the date as of which the record holders of
Series B Preferred Stock entitled to such dividends are to be determined.

        11. Stock to Be Reserved. The Company will at all times reserve and keep
available out of its authorized but unissued Series B Preferred Stock and Common
Shares, solely for the purpose of issue upon the exercise of this Warrant as
herein provided, such number of shares of (a) Series B Preferred Stock as shall
be issuable upon exercise of this Warrant, and (b) Common Shares as shall be
issuable upon conversion of the Series B Preferred Stock issuable upon exercise
of this Warrant (collectively, the "Reserved Shares"). The Company covenants
that, when the Reserved Shares are issued in accordance with the terms hereof
(including payment of the Exercise Price) or the terms of the Certificate of
Designations, Preferences and Rights of the Series B Preferred Stock (the
"Series B Certificate"), as applicable, the Reserved Shares shall be duly and
validly issued and fully paid and nonassessable and free from all taxes, liens
and charges with respect to the issue thereof. Without limiting the generality
of the foregoing, the Company covenants that it will from time to time take all
such action as may be reasonably necessary to assure that the par value per
share (as opposed to the Stated Value) of the Shares at all times equal to or
less than the effective Exercise Price.

        The Company will take all such action as may be reasonably necessary to
assure that all Reserved Shares may be issued without violation of any
applicable law or regulation, or of any requirements of any national securities
exchange upon which the Common Shares of the Company may be listed. The Company
will not take any action which results in any adjustment of the Exercise Price
if the total number of shares of Series B Preferred Stock issued and issuable
after such action upon exercise of this Warrant would exceed the total number of
shares of Series B Preferred Stock

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then authorized by the Company's Articles of Incorporation. The Company has not
granted and will not grant any right of first refusal or similar right with
respect to Shares issuable upon exercise of this Warrant, and there are no
preemptive rights associated with such Shares.

        12. Issue Tax. The issuance of certificates for shares of Series B
Preferred Stock upon exercise of this Warrant shall be made without charge to
the Holder for any issuance or transfer tax in respect thereof; provided that
the Company shall not be required to pay any tax which may be payable in respect
of any transfer involved in the issuance and delivery of any certificate in a
name other than that of the Holder.

        13. Closing of Books. The Company will at no time close its transfer
books against the transfer of the shares of Series B Preferred Stock issued or
issuable upon the exercise of this Warrant in any manner which interferes with
the timely exercise of this Warrant.

        14. Notices of Record Dates. If:

               (a) the Company sets a record date for holders of any class of
securities for the purpose of determining the holders entitled to receive any
dividend or other distribution (other than cash dividends out of earned
surplus), or any right to subscribe for, purchase or otherwise acquire any
shares of stock of any class or any other securities or property, or to receive
any other right, or

               (b) any Liquidation Event (as defined in the Series B
Certificate) occurs, then at least twenty (20) days, or such shorter period as
is practicable but in no event less than ten (10) days, before any such record
date or Liquidation Event, the Company shall give notice (the "Notice") to the
Holder specifying (i) the date on which such record is to be taken, and (ii) the
date on which such Liquidation Event is to take place, and the time, if any is
to be fixed, as of which the holders of record of Series B Preferred Stock or
Common Shares will be entitled to exchange their shares of Series B Preferred
Stock or Common Shares, as the case may be, for securities or other property
deliverable upon such Liquidation Event. The Notice shall state whether the
Liquidation Event or the record date is subject to the effectiveness of a
registration statement under the Securities Act of 1933, as amended (the
"Securities Act") or to a favorable vote of stockholders, if either is required.

        15. Registration Rights. The rights of the Holder with respect to the
registration under the Securities Act of the Common Shares issuable upon
conversion of the Shares are set forth in the Registration and Information
Rights Agreement dated as of the date hereof among the Company and the parties
thereto (the "Registration Rights Agreement").

        16. Warrant Transferrable. Subject to compliance with (i) applicable
state and federal securities laws, and (ii) any transfer restrictions set forth
in the Series B Certificate, the Registration Rights Agreement, the Shareholders
Agreement dated as of the date hereof among the Company and the parties thereto,
and the Stock Purchase Agreement dated as of the date hereof among the Company
and the parties thereto (collectively, the "Transaction Documents"), this
Warrant and the Holder's

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rights hereunder are transferrable, in whole or in part, without charge to the
Holder upon surrender of this Warrant with a properly executed assignment, in
form and substance reasonably acceptable to the Company.

        17. Notice of Adjustments: Notices. Whenever the Exercise Price or
number or type of securities issuable hereunder shall be adjusted pursuant to
Section 10 hereof, the Company shall issue and provide to the Holder a
certificate signed by an officer of the Company setting forth, in reasonable
detail, the event requiring the adjustment, the amount of the adjustment, the
method by which such adjustment was calculated and the Exercise Price and number
of Shares purchasable hereunder after giving effect to such adjustment.

        18. Governing Law. This Warrant shall be binding upon any successors or
assigns of the Company. This Warrant shall constitute a contract under the laws
of Illinois and for all purposes shall be construed in accordance with and
governed by the laws of said state, without giving effect to the conflict of
laws principles.

        19. Attorneys' Fees. In any litigation, arbitration or court proceeding
between the Company and the Holder relating hereto, the prevailing party shall
be entitled to reasonable attorneys' fees and expenses incurred in enforcing
this Warrant.

        20. Amendments. This Warrant may be amended and the observance of any
term of this Warrant may be waived only with the written consent of the Company
and the Holder.

        21. Notice. Except as otherwise specified herein, any notice, demand or
request required or permitted to be given pursuant to the terms of this
Agreement shall be in writing and shall be deemed given (i) when delivered
personally or by verifiable facsimile transmission (with a hard copy to follow)
on or before 5:00 p.m., central time, on a business day or, if the day is not a
business day, on the next succeeding business day, (ii) on the next business day
after timely delivery to an overnight courier and (iii) on the third business
day after deposit in the U.S. mail (certified or registered mail, return receipt
requested, postage prepaid), addressed as follows:

               If to the Company:

               Universal Access, Inc.
               100 North Riverside Plaza
               Suite 2200 Chicago, IL 60606
               Phone: 312-660-5000
               Fax: 312-660-5050

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               With a copy to:

               Shefsky & Froelich Ltd.
               444 North Michigan Avenue
               Suite 2500
               Chicago, Illinois 60611
               Attn: Mitchell D. Goldsmith, Esq.
               Phone: 312-836-4006
               Fax: 312-527-3194

and if to any Holder, at its address as shown on the stock records of the
Company or such other address as any such party shall deliver to the Company.

        22. Entire Agreement. This Warrant, the Notice of Exercise attached
hereto and the Transaction Documents contain the entire agreement between the
parties with respect to the subject matter hereof and supersede all prior and
contemporaneous arrangements or undertakings with respect thereto.

        IN WITNESS WHEREOF, Universal Access, Inc. has caused this Warrant to be
executed by its duly authorized officer.

Dated: February 5, 1999

                                            UNIVERSAL ACCESS, INC.

                                            By: /s/ PATRICK SHUTT
                                                --------------------------------
                                            Name: Patrick Shutt
                                            Title: President

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<PAGE>   9

                               NOTICE OF EXERCISE

To:     Universal Access, Inc.

        1. The undersigned hereby elects to purchase ____________________ shares
(the "Shares") of Series B Cumulative Convertible Preferred Stock, Stated Value
of $3.00 per shares of Universal Access, Inc. (the "Company") pursuant to the
terms of the attached Warrant, and tenders herewith payment of the purchase
price.

        2. The Shares to be received by the undersigned upon exercise of the
Warrant are being acquired for its own account, not as a nominee or agent, and
not with a view to resale or distribution of any part thereof, and the
undersigned has no present intention of selling, granting any participation in,
or otherwise distributing the same, except in compliance with applicable federal
and state securities laws. The undersigned further represents that it does not
have any contract, undertaking, agreement or arrangement with any person to
sell, transfer or grant participation to such person or to any third person,
with respect to the Shares. The undersigned has received all the information it
considers necessary or appropriate for deciding whether to purchase the Shares.

        3. The undersigned understands that the Shares are characterized as
"restricted securities" under the federal securities laws inasmuch as they are
being acquired from the Company in transactions not involving a public offering
and that under such laws and applicable regulations such securities may be
resold without registration under the Securities Act of 1933, as amended (the
"Act"), only in certain limited circumstances. In this connection, the
undersigned represents that it is familiar with Rule 144 of the Act, as
presently in effect, and understands the resale limitations imposed thereby and
by the Act.

        4. The undersigned understands the certificates evidencing the Shares
may bear one or all of the following legends:

               (a) "THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE
               SECURITIES ACT OF 1933. THEY MAY NOT BE SOLD, OFFERED FOR SALE,
               PLEDGED OR HYPOTHECATED IN THE ABSENCE OF A REGISTRATION
               STATEMENT IN EFFECT WITH RESPECT TO THE SECURITIES UNDER SUCH ACT
               OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH
               REGISTRATION IS NOT REQUIRED OR UNLESS SOLD PURSUANT TO RULE 144
               OF SUCH ACT."

               (b) Any legend required by applicable state law.

<PAGE>   10

        5. Please issue a certificate or certificates representing said Shares
in the name of the undersigned.

                                        [NAME OF HOLDER]

                                        By:
--------------------                       -------------------------------------
        Date                            Title:
                                              ----------------------------------

        6. Please issue a new Warrant for the unexercised portion of the
attached Warrant in the name of the undersigned.

                                        [NAME OF HOLDER]

                                        By:
--------------------                       -------------------------------------
        Date                            Title:
                                              ----------------------------------

                                       2<PAGE>   1

                                                                     EXHIBIT 4.8

THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
AMENDED, OR ANY STATE SECURITIES LAWS. THEY HAVE BEEN ACQUIRED SOLELY FOR
INVESTMENT AND NOT WITH A VIEW TO, OR IN CONNECTION WITH, THE SALE OR
DISTRIBUTION THEREOF. THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED,
HYPOTHECATED OR OTHERWISE DISTRIBUTED IN THE ABSENCE OF AN EFFECTIVE
REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF COUNSEL, SATISFACTORY IN
FORM AND SUBSTANCE TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED AND ANY APPLICABLE STATE SECURITIES LAWS.

No. E-1                                                        November 10, 1999

                                     WARRANT

        To Purchase 40,000 Shares of Series E Cumulative Convertible Preferred
Stock of Universal Access, Inc. (the "Company")

        1. Number of Shares: Exercise Price; Term. This certifies that Advanced
Equities, Inc. or its permitted assigns (the "Holder") is entitled, upon the
terms and subject to the conditions hereinafter set forth, at any time after the
date hereof and at or prior to 11:59 p.m. Central Time, on November 10, 2004
(the "Expiration Time"), but not thereafter, to acquire from the Company, in
whole or in part, from time to time, up to 40,000 fully paid and non-assessable
shares (the "Shares") of Series E Cumulative Convertible Preferred Stock, par
value $0.01 per share of the Company ("Series E Preferred Stock"), at a purchase
price of Eighteen dollars and thirty cents ($18.30) per Share (the "Exercise
Price"). The number of Shares, type of security for which this Warrant is
exercisable and Exercise Price are subject to adjustment as provided herein, and
all references to "Series E Preferred Stock" and "Exercise Price" herein shall
be deemed to include any such adjustment or series of adjustments.

        2. Exercise of Warrant.

        (a) In general, the purchase rights represented by this Warrant are
exercisable by the Holder, in whole or in part, at any time, or from time to
time, prior to the Expiration Time, by the surrender of this Warrant and the
Notice of Exercise annexed hereto, all duly completed and executed on behalf of
the Holder, at the office of the Company in Chicago, Illinois, (or such other
office or agency of the Company as it may designate by notice in writing to the
Holder at the address of the Holder appearing on the books of the Company), and
upon payment of the Exercise Price for the Shares thereby purchased (by cash,
certified or cashier's check, or wire transfer payable to the order of the
Company, at the time of exercise in an amount equal to the purchase price of the
Shares thereby purchased or by net issue exercise pursuant to Section 2(b)
hereof). Thereupon the Holder shall be entitled to receive from the Company a
stock certificate in proper form representing the number of Shares so purchased,
and a new Warrant in substantially identical form and dated as of such exercise
for the purchase of that number

<PAGE>   2

              X = Y (A-B)
                  -------
                     A

      Where          X=   the number of shares of Series E Preferred Stock to be
                          issued to the Holder

                     Y=   the number of shares of Series E Preferred Stock
                          purchasable under the Warrant, or if only a portion of
                          the Warrant is being exercised, the portion of the
                          Warrant being exercised and canceled (at the date of
                          such calculation)

                     A=   the Fair Market Value

                     B=   the Exercise Price

of Shares equal to the difference, if any, between the number of Shares subject
hereto and the number of Shares as to which this Warrant is so exercised.

        (b) Net Issue Exercise. Notwithstanding any provisions in this Warrant
to the contrary, if the fair market value of one share of Series E Preferred
Stock (the "Fair Market Value") is greater than the Exercise Price (at the date
of calculation as set forth below), in lieu of exercising this Warrant by paying
the Exercise Price in cash, the Holder may elect to receive shares equal to the
value (as determined below) of this Warrant (or the portion of the Warrant being
exercised and canceled) by surrender of this Warrant at the principal office of
the Company together with the properly endorsed Notice of Exercise and notice of
such election, in which event the Company shall issue to the Holder a number of
shares of Series E Preferred Stock computed using the following formula:

For purposes of the above calculation, the Fair Market Value shall be determined
by the Company's Board of Directors in good faith; provided, however, that where
there exists a public market for the Company's common shares, no par value per
share (the "Common Shares") at the time of such exercise, the Fair Market Value
shall be the product of (i) the average of the closing bid and asked prices of
the Common Shares quoted in the Over-The-Counter Market Summary or the last
reported sale price of the Common Shares or the closing price quoted on the
NASDAQ National Market or on any exchange on which the Common Shares are listed,
whichever is applicable, as published in the Central Edition of The Wall Street
Journal for the five (5) trading days prior to the date of determination of Fair
Market Value and (ii) the number of Common Shares into which each share of
Series E Preferred Stock is convertible at the time of such exercise
Notwithstanding the foregoing, if the Warrant is exercised in connection with
the Company's initial public offering of Common Shares, the Fair Market Value
shall be the product of (i) the per share offering price to the public of the
Company's initial public offering, and (ii) the number of Common Shares into
which each share of Series E Preferred Stock is convertible at the time of such
exercise.

<PAGE>   3

        3. Issuance of Shares. Certificates for Shares purchased hereunder shall
be delivered to the Holder within a reasonable time after the date on which this
Warrant shall have been exercised in accordance with the terms hereof.
All Shares that may be issued upon the exercise of this Warrant shall, upon such
exercise, be duly and validly authorized and issued, fully paid and
non-assessable and free from all taxes, liens and charges in respect of the
issuance thereof (other-than liens or charges created by or imposed upon the
Holder or taxes in respect of any transfer occurring contemporaneously or
otherwise specified herein). The Company agrees that the Shares so issued shall
be and shall for all purposes be deemed to have been issued to the Holder as the
record owner of such Shares as of the close of business on the date on which
this Warrant shall have been exercised or converted in accordance with the terms
hereof.

        4. No Fractional Shares or Scrip. No fractional Shares or scrip
representing fractional Shares shall be issued upon the exercise of this
Warrant. In lieu of any fractional Share to which the Holder would otherwise be
entitled, the Holder shall be entitled, at its option, to receive either (i) a
cash payment equal to the excess of fair market value for such fractional Share
above the Exercise Price for such fractional Share (as determined in good faith
by the Company) or (ii) a whole Share if the Holder tenders the Exercise Price
for one whole share.

        5. No Rights as Shareholders. This Warrant does not entitle the Holder
to any voting rights or other rights as a shareholder of the Company prior to
the exercise hereof.

        6. Charges. Taxes and Expenses. Certificates for Shares issued upon
exercise of this Warrant shall be issued in the name of the Holder. Issuance of
certificates for Shares upon the exercise of this Warrant shall be made without
charge to the Holder for any issue or transfer tax or other incidental expense
in respect of the issuance of such certificates, all of which taxes and expenses
shall be paid by the Company.

        7. Exchange and Registry of Warrant. This Warrant is exchangeable, upon
the surrender hereof by the registered Holder at the office or agency of the
Company referenced in Section 2 above, for a new Warrant in substantially
identical form and dated as of such exchange. The Company shall maintain at the
office or agency referenced in Section 2 above, a registry showing the name and
address of the registered Holder of this Warrant. This Warrant may be
surrendered for exchange or exercise, in accordance with its terms, at the
office of the Company, and the Company shall be entitled to rely in all
respects, prior to written notice to the contrary, upon such registry.

        8. Loss, Theft, Destruction or Mutilation of Warrant. Upon receipt by
the Company of evidence reasonably satisfactory to it of the loss, theft,
destruction or mutilation of this Warrant, and in the case of loss, theft or
destruction, of indemnity or security reasonably satisfactory to it, and upon
reimbursement to the Company of all reasonable expenses incidental thereto, and
upon surrender and cancellation of this

<PAGE>   4

Warrant, if mutilated, the Company will make and deliver a new Warrant of like
tenor and dated as of such cancellation and reissuance, in lieu of this Warrant.

        9. Saturdays, Sundays. Holidays, etc. If the last or appointed day for
the taking of any action or the expiration of any right required or granted
herein shall be a Saturday or a Sunday. or shall be a legal holiday, then such
action may be taken or such right may be exercised on the next succeeding day
not a Saturday or a Sunday or a legal holiday.

        10. Adjustments of Rights. The purchase price per Share and the number
of Shares purchasable hereunder are subject to adjustment from time to time as
follows:

                (a) Merger or Consolidation. If at any time there shall be a
merger or a consolidation of the Company with or into another corporation when
the Company is not the surviving corporation, then, as a condition of such
merger or consolidation, lawful provision shall be made so that the Holder shall
thereafter be entitled to receive upon exercise of this Warrant, during the
period specified herein and upon payment of the aggregate Exercise Price then in
effect, the number of shares of stock or other securities or property (including
cash) of the successor corporation resulting from such merger or consolidation,
to which the holder of the stock deliverable upon exercise of this Warrant would
have been entitled in such merger or consolidation if this Warrant had been
exercised immediately before such merger or consolidation. In any such case,
appropriate adjustment shall be made in the application of the provisions of
this Warrant with respect to the rights and interests of the Holder after the
merger or consolidation. This provision shall apply to successive mergers or
consolidations,

                (b) Reclassification, Recapitalization. etc, If the Company at
any time shall, by subdivision, combination or reclassification of securities,
recapitalization, automatic conversion, or other similar event affecting the
number or character of outstanding Shares, or otherwise, change any of the
securities as to which purchase rights under this Warrant exist into the same or
a different number of securities of any other class or classes, this Warrant
shall thereafter represent the right to acquire such number and kind of
securities as would have been issuable as the result of such change with respect
to the securities that were subject to the purchase rights under this Warrant
immediately prior to such subdivision, combination, reclassification or other
change.

                (c) Split, Subdivision or Combination of Shares. If the Company
at any time while this Warrant remains outstanding and unexpired shall split,
subdivide or combine the securities as to which purchase rights under this
Warrant exist, the Exercise Price shall be proportionately decreased in the case
of a split or subdivision or proportionately increased in the case of a
combination.

                (d) Stock Dividends. If the Company at any time while this
Warrant is outstanding and unexpired shall pay a dividend with respect to Series
E Preferred Stock payable solely in shares of the Company's equity securities,
then the Exercise Price shall be adjusted, from and after the date of
determination of the shareholders entitled to

<PAGE>   5

receive such dividend, to that price determined by multiplying the Exercise
Price in effect immediately prior to such date of determination by a fraction
(i) the numerator of which shall be the total number of Common Shares
outstanding immediately prior to such dividend, and (ii) the denominator of
which shall be the total number of Common Shares outstanding immediately after
such dividend.

        The number of Common Shares at any time outstanding (A) shall include,
in addition to outstanding Common Shares, the number of Common Shares into which
the Series A Preferred Stock, the Series B Cumulative Convertible Preferred
Stock, the Series C Convertible Preferred Stock, the Series D Cumulative
Convertible Preferred Stock, the Series E Preferred Stock or any of the
Company's other equity securities, indebtedness or other securities are
convertible; (B) shall include the number of Common Shares into which any of the
Company's vested options or warrants (including warrants exercisable for equity
securities or indebtedness convertible into Common Shares) are then convertible;
and (B) shall not include treasury shares. This paragraph shall apply only if
and to the extent that, at the time of such event, this Warrant is then
exercisable for Series E Preferred Stock,

                (e) Adjustment of Number of Shares. Upon each adjustment in the
Exercise Price pursuant to 10(c) or 10(d) hereof, the number of Shares
purchasable hereunder shall be adjusted, to the nearest whole Share, to the
product obtained by multiplying the number of Shares purchasable immediately
prior to such adjustment in the Exercise Price by a fraction (i) the numerator
of which shall be the Exercise Price immediately prior to such adjustment, and
(ii) the denominator of which shall be the Exercise Price immediately after such
adjustment.

                (f) Dividends. If the Company declares or pays a dividend or
other distribution upon the Series E Preferred Stock other than a stock dividend
payable solely in shares of the Company's equity securities (a "Dividend"), then
the Company shall pay to the Holder at the time of payment thereof the Dividend
which would have been paid to such Holder if such Holder had held the maximum
number of Shares acquirable upon complete exercise of the outstanding portion of
this Warrant immediately prior to the date on which a record is taken for such
Dividend, or, if no record is taken, the date as of which the record holders of
Series B Preferred Stock entitled to such dividends are to be determined

        11. Stock to Be Reserved. The Company will at all times reserve and keep
available out of its authorized but unissued Series E Preferred Stock and Common
Shares, solely for the purpose of issue upon the exercise of this Warrant as
herein provided, such number of shares of (a) Series E Preferred Stock as shall
be issuable upon exercise of this Warrant, and (b) Common Shares as shall be
issuable upon conversion of the Series E Preferred Stock issuable upon exercise
of this Warrant (collectively, the "Reserved Shares"). The Company covenants
that, when the Reserved Shares are issued in accordance with the terms hereof
(including payment of the Exercise Price) or the terms of the Certificate of
Designations, Preferences and Rights of the Series E Preferred

<PAGE>   6

Stock (the "Series E Certificate"), as applicable, the Reserved Shares shall be
duly and validly issued and fully paid and non-assessable and free from all
taxes, liens and charges with respect to the issue thereof Without limiting the
generality of the foregoing, the Company covenants that it will from time to
time take all such action as may be reasonably necessary to assure that the par
value per share (as opposed to the Stated Value) of the Shares at all times
equal to or less than the effective Exercise Price.

        The Company will take all such action as may be reasonably necessary to
assure that all Reserved Shares may be issued without violation of any
applicable law or regulation, or of any requirements of any national securities
exchange upon which the Common Shares of the Company may be listed. The Company
will not take any action which results in any adjustment of the Exercise Price
if the total number of shares of Series E Preferred Stock issued and issuable
after such action upon exercise of this Warrant would exceed the total number of
shares of Series E Preferred Stock then authorized by the Company's Certificate
of Incorporation.

        12. Issue Tax. The issuance of certificates for shares of Series E
Preferred Stock upon exercise of this Warrant shall be made without charge to
the Holder for any issuance or transfer tax in respect thereof; provided that
the Company shall not be required to pay any tax which may be payable in respect
of any transfer involved in the issuance and delivery of any certificate in a
name other than that of the Holder.

        13. Closing of Books. The Company will at no time close its transfer
books against the transfer of the shares of Series E Preferred Stock issued or
issuable upon the exercise of this Warrant in any manner which interferes with
the timely exercise of this Warrant.

        14. Notices of Record Dates. If:

                (a) the Company sets a record date for holders of any class of
securities for the purpose of determining the holders entitled to receive any
dividend or other distribution (other than cash dividends out of earned
surplus), or any right to subscribe for, purchase or otherwise acquire any
shares of stock of any class or any other securities or property, or to receive
any other right, or

                (b) and Liquidation Event (as defined in the Series E
Certificate) occurs,

then at least twenty (20) days, or such shorter period as is practicable but in
no event less than ten (10) days, before any such record date or Liquidation
Event, the Company shall give notice (the "Notice") to the Holder specifying (i)
the date on which such record is to be taken, and (ii) the date on which such
Liquidation Event is to take place, and the time, if any is to be fixed, as of
which the holders of record of Series E Preferred Stock or Common Shares will be
entitled to exchange their shares of Series E Preferred Stock or Common Shares,
as the case may be, for securities or other property deliverable upon such
Liquidation Event. The Notice shall state whether the Liquidation Event or the

<PAGE>   7

record date is subject to the effectiveness of a registration statement under
the Securities Act of 1933, as amended (the "Securities Act") or to a favorable
vote of stockholders, if either is required.

        15. Registration Rights. The rights of the Holder with respect to the
registration under the Securities Act of the Common Shares issuable upon
conversion of the Shares are set forth in the Registration Rights Agreement
dated as of the date hereof among the Company and the parties thereto (the
"Registration Rights Agreement").

        16. Warrant Transferable. Subject to compliance with (i) applicable
state and federal securities laws, and (ii) any transfer restrictions set forth
in the Series E Certificate, the Registration Rights and the Shareholders
Agreement dated as of the date hereof among the Company and the parties
(collectively, the "Transaction Documents"), this Warrant and the Holder's
rights hereunder are transferable, in whole or in part, without charge to the
Holder upon surrender of this Warrant with a properly executed assignment, in
form and substance reasonably acceptable to the Company.

        17. Notice of Adjustments; Notices. Whenever the Exercise Price or
number or type of securities issuable hereunder shall be adjusted pursuant to
Section 10 hereof, the Company shall issue and provide to the Holder a
certificate signed by an officer of the Company setting forth, in reasonable
detail, the event requiring the adjustment, the amount of the adjustment, the
method by which such adjustment was calculated and the Exercise Price and number
of Shares purchasable hereunder after giving effect to such adjustment.

        18. Governing Law. This Warrant shall be binding upon any successors or
assigns of the Company. This Warrant shall constitute a contract under the laws
of Delaware and for all purposes shall be construed in accordance with and
governed by the laws of said state, without giving effect to the conflict of
laws principles.

        19. Attorneys' Fees. In any litigation, arbitration or court proceeding
between the Company and the Holder relating hereto, the prevailing party shall
be entitled to reasonable attorneys' fees and expenses incurred in enforcing
this Warrant.

        20. Amendments. This Warrant may be amended and the observance of any
term of this Warrant may be waived only with the written consent of the Company
and the Holder.

        21. Notice. Except as otherwise specified herein, any notice, demand or
request required or permitted to be given pursuant to the terms of this
Agreement shall be in writing and shall be deemed given (i) when delivered
personally or by verifiable facsimile transmission (with a hard copy to follow)
on or before 5:00 p.m., central time, on a business day or, if the day is not a
business day, on the next succeeding business day, (ii) on the next business day
after timely delivery to an overnight courier and (iii) on the third business
day after deposit in the U.S. mail (certified or registered mail, return receipt
requested, postage prepaid), addressed as follows:

<PAGE>   8

        If to the company:

        Universal Access, Inc.
        100 North Riverside Plaza
        Suite 2200
        Chicago, EL 60606
        Phone: 312-660-5000
        Fax:   312-660-5050

        With a copy to:

        Shefsky & Froelich Ltd.
        444 North Michigan Avenue
        Suite 2500
        Chicago, IL 60611
        Attn:  Mitchell D. Goldsmith, Esq.
        Phone: 312-836-4006
        Fax:   312-527-3194

and if to any Holder, at its address as shown on the stock records of the
Company or such other address as any such party shall deliver to the Company.

        22. Entire Agreement. This Warrant, the Notice of Exercise attached
hereto and the Transaction Documents contain the entire agreement between the
parties with respect to the subject matter hereof and supersede all prior and
contemporaneous arrangements or undertakings with respect thereto.

IN WITNESS WHEREOF, Universal Access, Inc. has caused this Warrant to be
executed by its duly authorized officer.

Dated: November 10, 1999

                                            UNIVERSAL ACCESS, INC.

                                            By: /s/ PATRICK SHUTT
                                               ---------------------------------
                                            Name: Patrick Shutt
                                            Title: President and CEO

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