역시 DOW의 홈페이지 FAQ에 나오는데요,
엑스칼리버는 퀘스트를 끝낸 사람이 갖습니다.
다만 생명점 추가와 흰카드는 퀘스트에 있는 사람만 받습니다.

"What happens if a Knight not on Excalibur plays the Lady of the Lake to end that Quest without being present there?

This Knight is the one that receives Excalibur, because he is the one who completed the Quest.. However, he does not receive any life point and does not share in the White cards received as a result of the Quest's completion, because he is not present on the Quest itself.
The other knights present on Excalibur, if any, share the White cards, and each get a life point. If no knight is present on the Quest, then no life point is gained, and the White cards are simply drawn and discarded! If no agreement is reached during the sharing, the cards are dealt randomly to the knights present on the Quest, starting with the Knight's of the Lady of the Lake's player's choice."