Whom do you register with? The government? The party in question? Can you change your registration?
I get the feeling things are different in Canada. You just "become a member" of a party. Probably involves a fee paid to said party. Then you can attend conventions and vote on the leader. I'm not clear on what happens if two people from one party want to run in a particular riding. I think the members in that riding get to vote on who should run. That kind of sounds like what you're talking about.
But it may be that you can be a member of many parties, if you want, especially considering that some parties don't exist on both federal and provincial levels. This is something I'm not sure about. You might be a member of the Parti Quebecois provincially but the Bloc Qubecois federally (or is it the other way around - Bel?). Or Liberal in both, since it exists at both levels. All very confusing...
