1. In law, to hear, to settle, and to decide a legal case or to reach a judicial conclusion about something: After hearing both sides of the divorce case involving the children, the judge adjudicated the matter and gave the mother full custody of her offspring.
2. To make an official judgement about a problem or a dispute in a law case: The two families were constantly arguing about the fence along their property lines causing them to go to court. The judge adjudicated the conflict and ordered the fence to be taken down.
3. Etymology: from Latin ad-, "to" + judicare, "to judge".