[Question] What would happen if all the water on Earth were accumulated into spheres & drop on the surface?

I was inspired by the APOD pictures and discussion here and here. The conditions for the ‘experiment’ are:

  • For some mysterious reason, all the water on Earth (minus that in living things—the biosphere) suddenly & immediately converges into 17 identical sphere and let to drop down to the land below right away.

  • The places of those water balls are the centers of 17 biggest tectonic plates as listed here.

  • The bottoms of the huge balls just touch the highest points on the ground there. Also from my calculation, which may be wrong, their radius is 258 km.

  • The ISS is currently at its highest altitude of 460 km with ship(s) in dock.

So, what will happen to us, the Earth and things on it?

My prediction is very grim for humanity, thus I turn to the ISS as our last hope. Supposed that at t=0, the astronauts can choose the station’s direction of flying. Can they avoid all the 17 falling balls? Is there any chance they can land back on Earth without any help from Houston when things settle down, in case the water does settle down and not all turn into vapor? (That’s a possibility I can’t calculate and will need your help).

I’m looking for answers in xkcd style, which IMO is a textbook way to respond to absurd “What if?” questions. It’s detailed, with nice pictures to help our imagination, displaying formulas when necessary but also very rookie-friendly, tackle the problem from many different angles & POVs, and takes into account some easy-to-overlook stuffs. Too bad he doesn’t answer anymore.

Anyway, thank you just for reading! :)