Verbs:
* Adjudicating (present participle)
* Adjudicated (past tense and past participle)
* Adjudicates (third-person singular present tense)
Nouns:
* Adjudication (the act of adjudicating)
* Adjudicator (one who adjudicates)
Adjectives:
* Adjudicative (relating to adjudication)
Other related words:
* Arbitrate (to settle a dispute)
* Mediate (to help parties reach an agreement)
* Judge (to make a decision in a legal case)
* Determine (to decide something with certainty)
* Settle (to resolve a dispute)
These words all relate to the concept of making a decision or resolving a conflict, but they may have slightly different nuances depending on the context.