Space is controlled by nations and their military so I don't see why there will not be conflicts and escalations. Only way to prevent war in space is humans not going to space.
It's not per see controlled. Once we get strong enough drives, then space is too big to be effectively controlled by anyone. Some planets or objects may, but many others won't be.
The war in orbit though, that will likely happen sooner rather than later.
The war in orbit though, that will likely happen sooner rather than later.