ZeroEx
Newcomer
I think it will be full installs, but the OS will back up the contents to the cloud and free up space when necessary. It's reasonable to assume that most games will be playable with a minimum base install size, something like 2 to 5GB, of which you can keep hundreds on the HDD locally. Then whatever you start to play will automatically re-download the erased parts from the cloud in the background.
I think full install as well. But partial installs when you're playing the game so that you don't have to wait until the game is fully installed to start playing. This will work well online and offline.
Maybe the system (depending on how games developers make their games) can erase portions of the game that you don't play over time, to free up HDD space.