Rockall, a hitherto uninhabited island in the Atlantic some 300 miles west of Scotland, has been occupied by an Englishman. Ownership of the rock is a matter of dispute among the UK, Ireland and Denmark (on behalf of the Faeroes),
But, according to the Island of Rockall Act 1972, it is a part of Scotland (specifically, part of Inverness-shire). Accordingly, if Scotland were to gain its independence, it could be the start of a Scottish Empire.
Does it matter? Probably not. According to the UN Law of the Sea, the rights to economic exploitation of the seas around uninhabited islands are severely limited.