adjudicate

(verb) put on trial or hear a case and sit as the judge at the trial of. Synonyms: judge, try. Examples: "The football star was tried for the murder of his wife." "The judge tried both father and son in separate trials."

(verb) bring to an end; settle conclusively. Synonyms: decide, settle, resolve. Examples: "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."