The Collaborative International Dictionary of English v.0.48:

Adjudicate \Ad*ju"di*cate\, v. t. [imp. & p. p. Adjudicated;
   p. pr. & vb. n. Adjudicating] [L. adjudicatus, p. p. of
   adjudicare. See Adjudge.]
   To adjudge; to try and determine, as a court; to settle by
   judicial decree.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Adjudicate \Ad*ju"di*cate\, v. i.
   To come to a judicial decision; as, the court adjudicated
   upon the case.
   [1913 Webster]

WordNet (r) 3.0 (2006):

adjudicate
    v 1: put on trial or hear a case and sit as the judge at the
         trial of; "The football star was tried for the murder of
         his wife"; "The judge tried both father and son in separate
         trials" [syn: judge, adjudicate, try]
    2: bring to an end; settle conclusively; "The case was decided";
       "The judge decided the case in favor of the plaintiff"; "The
       father adjudicated when the sons were quarreling over their
       inheritance" [syn: decide, settle, resolve,
       adjudicate]

Moby Thesaurus II by Grady Ward, 1.0:

21 Moby Thesaurus words for "adjudicate":
   account, adjudge, allow, arbitrate, be judicious, consider, count,
   deem, esteem, exercise judgment, express an opinion,
   form an opinion, hold, judge, pine, presume, referee, regard,
   suppose, think of, unique