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theres events that fire that give u core provinces. I have no idea what causes them though, but as britain a lot of canada and india is now more core through those events so i guess it just fires eventually.
 
I think its random. I've gotten cores on captured territory within a month or two, or it can take years. I dont know if there is a "turns into a core if captured for xx years" function.
 
The generic event that gives cores only fires if you have Nationalism and Imperialism researched AND are a Greater Power. The average time (MTTH) is 10 years, and there are several modifiers that make it more or less likely, the main one being that Colonial States take 10 times as long.
 
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