Batman in the 30th Century

Hearing about the United Planets in Superman got me wondering what is Batman's place in the 30th century? Now I know by then he and everyone associated with him would be dead but what would he and the Batfamily leave behind? What sort of legacy would they have in the 30th Century? Has any of it been mentioned or shown before? Thought on this?

Batman # 26 (1,943) # 67 (1,951) and Detective Comics 216 (1,955) featured a future Batman in the year 3,000 to 3,055 but this was before crossover Universes so there were no other heroes, Most Golden Age heroes has their own universe continuity. The Atlantis Empire was ruled by a Robin relative