1) Act as a referee 2) Bring to an end 3) Decide 4) Determine 5) Hear a case 6) Hear in a courtly way 7) Judge 8) Referee 9) Referee at a court 10) Rule from the bench 11) Settle conclusively 12) To act as a judge 
• (v. t.) To adjudge; to try and determine, as a court; to settle by judicial decree. • (v. i.) To come to a judicial decision; as, the court adjudicated upon the case.
Ad·ju'di·cate transitive verb [ imperfect & past participle Adjudicated ; present participle & verbal noun Adjudicating ] [ Latin adjudicatus , past participle of adjudicare . See Adjudge .] To adjudge; to try and ...
adjudicate 1. In law, to hear and decide (a case), to reach a judicial decision about something; adjudge.2. Someone who serves as a judge and to make an official decision about a problem or dispute.
to hear or try and determine judicially
hear a case and sit as the judge at the trial of