I am playing as England, and I have conquered all of the British isles, and I even own the Netherlands and Belgium. I also have a small foothold in France by holding Calais and Picardie. Once I gained all this land, it was about 1510, and I decided to start colonizing. I swept through Greenland, Newfoundland, the thirteen colonies, and all of Hispaniola. In a war with Portugal and Castille, I gained the rest of the Caribbean islands, and I am in 2nd place.
The year is 1574, and I am wondering if any of my colonies can eventually become their own colonies and attempt to gain independence. If they can, should I be worried about it?