I agree with Sam, and will embellish a bit.
I think the nature of your government depends on the situation and the attitudes of your countries. I think, under normal circumstances, most countries would want to remain sovereign, although they might form a treaty. Especially if these countries were once separate worlds, they will have a very strong personal identity and probably won't want to sacrifice their government system, security, and way of life for a one-world government. If, however, a war or outside force threatened them, they might want to band together more closely. You could also have some kind of radical political reform movement sweep through that would make the people want to unite. Maybe one country conquered the other two. If they did unite of their own free will, the nature of their collaboration would determine whether they set up a high-king or simply worked together. There are other possibilities, also - like sending ambassadors to a council, for example.
So, I would ask yourself - what kind of political arrangement do you need to make your story work? Figure out what you need, and then write backstory to make it happen. Alternately, if you don't need a particular system for a storyline, I would look at your current set-up and decide what kind of union (or lack thereof) was most reasonable.