Wikipedia quotes an analysis by GM Harry Golombek (from Golombek’s Encyclopedia of Chess, Crown Publishers, 1977, p. 218. I do not have access to the source) where he lists possible handicaps, in order of increasing severity.
The last item in the list is "Strong king", where the king is given the ability to move up to two squares in any direction. It appears further down (that is, a bigger handicap) than "Queenside odds" where the stronger player gives up a queen, rook, knight and bishop.
I can understand that this is powerful because a strong king is harder to mate (AFAIK, even K+Q can't mate a strong king. Not only does he have more escape routes, the normal king can't get too close to the action) and in general is hard to put pressure against.
But seriously, more powerful than Q+R+B+N? Is this a mistake? If not, where can I find an analysis that supports this claim?
Edit: I've played a few games of this with friends. The jury is still out on the exact strength, but my estimation: This is probably on the same ballpark as queen odds, but nowhere near QRBN.