When does a super-Earth become a water world? Is it a mass/radius combination that creates this possibility?
By "water world" do you mean what EDG calls a panthalassic world, where the boundary between surface and atmosphere is a blur?
If that's your Q, I asked about that in a different thread somewhere, and I think a world could
be a panthalassic world under specific conditions:
1) Mass maybe 4+ total earth masses, with 2+ earth masses comprised of water. Like, lots of friggin' water, man. I'm not exactly sure how big it needs to be, but definitely bigger than Earth.
2) A density that would fit. If Earth as it is has a density of 5.52 g/cm3, and you add another whole earth mass of water, you get a density of 3.25 or so. If you're rolling randomly for density, a high mass world with low enough density might fit this classification.