Final answer:
The mechanism that determines whether a large icy planetesimal becomes a 'water world' or a gas giant involves violent impacts and heat generation, as well as the formation and migration of planets within protoplanetary disks.
Step-by-step explanation:
The mechanism that likely accounts for whether a large icy planetesimal becomes a 'water world' or a gas giant is the process of violent impacts and heat from radioactive elements. When planetesimals crash into each other and disrupt growing planets, the heat generated causes the planets to become liquid and gas and differentiate. This process helps explain their present internal structures.
Additionally, in the outer solar system where ices are present, protoplanets can grow to be much larger and attract surrounding gas. The hydrogen and helium collapse onto their cores and heat the giant planets, but they are too small to begin nuclear reactions like stars. Over time, these giant planets gradually cool to their present state.
Lastly, the presence of 'hot Jupiters' (jovian-sized exoplanets closer to their star than Mercury is to our Sun) can be explained by planet migrations within the protoplanetary disk or gravitational encounters between sibling planets that scatter one of the planets inward.