Upvote:3
As this question goes over, we are most likely not talking about a historical figure here. There are no contemporaneous sources testifying to his existence.
As a mythological figure, it depends greatly on which myths about him you credit. In the very first story he graced, Historia Brittonum, he was a mere military commander, which means he likely ruled little or no territory at all.
At the other extreme, Geoffrey of Monmouth's Historia Regum Britanniae depicted him as a proper Emperor, ruling over France, the British Isles, and Iceland.