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.
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            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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WordNet (r) 3.0 (2006):

assigning
    n 1: the act of distributing something to designated places or
         persons; "the first task is the assignment of an address to
         each datum" [syn: assignment, assigning]