I'm curious about this because I just read a story where a lawyer tried to sue Italy over the trial of Jesus, and failed because Italy isn't a legal successor to the Roman Empire. It would be interesting if there was, though. I mean, the Ottoman Sultans declared themselves to be Caesars and the Pope holds the title of Pontifex Maximus to this day. When did the last figure or entity with a reasonably broad recognition of their claim to govern/be the Roman empire exist?