To make an official decision about who is right in (a dispute) : to settle judicially. (Merriam – Webster)
To act as judge in a competition or argument, or to make a formal decision about something. (Cambridge Dictionary)
Make a formal judgement on a disputed matter. (Oxford Dictionaries)
If you adjudicate on a dispute or problem, you make an official judgement official or decision about it. (Collins Dictionary)
What does adjudicates mean?