verb

• (transitive) To decide, rule on, or settle as a judge.
  "From the twelfth century Shetland had been administered directly by the Norwegian crown through the 'foud', rather than forming part of the patrimony of a great aristocratic estate. The foud appointed 'underfouds' and the Shetlands evolved their own elected officers, a 'lawman' and parish 'lawrightmen', who adjudicated and negotiated the collection of customary taxes and fines on behalf of the local population."
• (intransitive, often followed by on) To act as a judge.
  "A Court of Arbitration, constituted by the World Bank in The Hague, has brushed aside New Delhi’s objections and concluded that it has the competence to adjudicate on Pakistan’s objection to the Kishenganga and Ralte hydroelectric projects of India."
• (Scots law, transitive, as of a debtor's estate) To seize or convey as security.