If you score a battlefield by conquering with a champion unit (Kaisa/Qiyana), then move that unit out and back to the same battlefield in the same turn, can you re-trigger the conquer abilities?

Ruling: No, you cannot score a battlefield more than once per turn. Since conquering is a form of scoring, you cannot conquer the same battlefield again in the same turn even if you move the unit out and back.

Nuances:

• If your score has its point replaced (e.g., drawing 1 if you can't win the final point), any conquer effects will still trigger in those replacement cases.