The Collaborative International Dictionary of English v.0.48:

Assign \As*sign"\, v. t. [imp. & p. p. Assigned; p. pr. & vb.
   n. Assigning.] [OE. assignen, asignen, F. assigner, fr. L.
   assignare; ad + signare to mark, mark out, designate, signum
   mark, sign. See Sign.]
   1. To appoint; to allot; to apportion; to make over.
      [1913 Webster]

            In the order I assign to them.        --Loudon.
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            The man who could feel thus was worthy of a better
            station than that in which his lot had been
            assigned.                             --Southey.
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            He assigned to his men their several posts.
                                                  --Prescott.
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   2. To fix, specify, select, or designate; to point out
      authoritatively or exactly; as, to assign a limit; to
      assign counsel for a prisoner; to assign a day for trial.
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            All as the dwarf the way to her assigned. --Spenser.
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            It is not easy to assign a period more eventful.
                                                  --De Quincey.
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   3. (Law) To transfer, or make over to another, esp. to
      transfer to, and vest in, certain persons, called
      assignees, for the benefit of creditors.
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   To assign dower, to set out by metes and bounds the widow's
      share or portion in an estate. --Kent.
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The Collaborative International Dictionary of English v.0.48:

Assign \As*sign"\, v. i. (Law)
   To transfer or pass over property to another, whether for the
   benefit of the assignee or of the assignor's creditors, or in
   furtherance of some trust.
   [Webster 1913 Suppl.]

The Collaborative International Dictionary of English v.0.48:

Assign \As*sign"\, n. [From Assign, v.]
   A thing pertaining or belonging to something else; an
   appurtenance. [Obs.]
   [1913 Webster]

         Six French rapiers and poniards, with their assigns, as
         girdles, hangers, and so.                --Shak.
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The Collaborative International Dictionary of English v.0.48:

Assign \As*sign"\, n. [See Assignee.] (Law)
   A person to whom property or an interest is transferred; as,
   a deed to a man and his heirs and assigns.
   [1913 Webster]

WordNet (r) 3.0 (2006):

assign
    v 1: give an assignment to (a person) to a post, or assign a
         task to (a person) [syn: delegate, designate, depute,
         assign]
    2: give out; "We were assigned new uniforms" [syn: assign,
       allot, portion]
    3: attribute or credit to; "We attributed this quotation to
       Shakespeare"; "People impute great cleverness to cats" [syn:
       impute, ascribe, assign, attribute]
    4: select something or someone for a specific purpose; "The
       teacher assigned him to lead his classmates in the exercise"
       [syn: assign, specify, set apart]
    5: attribute or give; "She put too much emphasis on her the last
       statement"; "He put all his efforts into this job"; "The
       teacher put an interesting twist to the interpretation of the
       story" [syn: put, assign]
    6: make undue claims to having [syn: arrogate, assign]
    7: transfer one's right to
    8: decide as to where something belongs in a scheme; "The
       biologist assigned the mushroom to the proper class" [syn:
       assign, attribute]

Moby Thesaurus II by Grady Ward, 1.0:

189 Moby Thesaurus words for "assign":
   abalienate, accredit, alien, alienate, allocate, allot, allow,
   amortize, apply, appoint, apportion, appropriate, appropriate to,
   ascribe, assign to, associate, attach, attribute, authorize,
   barter, bequeath, carry over, cede, charge, charter, choose,
   classify, collocate, commend, commission, commit, communicate,
   confer, confide, consign, convey, credit, decide, deed, deed over,
   define, delegate, deliver, demise, denominate, deploy, deport,
   depute, deputize, designate, destine, detach, detail, determine,
   devolute, devolve, devolve upon, diffuse, dispose, disseminate,
   distribute, earmark, emplace, empower, enfeoff, entrust, establish,
   exchange, expel, export, extradite, fate, fix, get a fix, give,
   give homework, give in charge, give in trust, give out,
   give title to, grant, hand, hand down, hand forward, hand on,
   hand over, home in on, impart, import, impute, indicate, infeudate,
   install, lay, lay down, license, link, localize, locate, lot,
   make a syllabus, make an assignment, make assignments, make over,
   mark, mark off, mark out for, mention, metastasize, metathesize,
   mete out, mission, name, navigate, negotiate, nominate, ordain,
   order, ordinate, pass, pass on, pass over, pass the buck, perfuse,
   pick out, pigeonhole, pin down, pinpoint, place, point out,
   portion off, position, post, prescribe, put, put down,
   put in place, refer, relate, relay, relegate, remand, remise,
   remit, reserve, restrict, restrict to, schedule, second, select,
   sell, send out, set, set a task, set apart, set aside, set hurdles,
   set off, settle, settle on, sign away, sign over, signify, situate,
   specialize, specify, spot, spread, state, stipulate, surrender,
   switch, tab, tag, trade, transfer, transfer property, transfuse,
   translate, translocate, transmit, transplace, transplant,
   transpose, triangulate, trust, turn over, warrant, zero in on