If you do something impartially, you do it without taking a side — you judge, decide, listen, or speak in a fair way. It is simply the adverb of impartial: it tells you how the action is done. A teacher who marks papers impartially uses the same standard for every student. A reporter who writes impartially does not load the story to help one party. It is a rather formal word; in easy talk people say “fairly” or “evenly.” Fairly is broader, though (it can also mean “quite”). Impartially is narrower: it always means “not choosing a team.” You place it with the verb: decide impartially, treat them impartially, be judged impartially.