Our understanding is that you can own whatever you want, wherever you wish...BUT.... be prepared for the possibility of tax problems at some point. Each state wants to claim you for their own tax purposes.
What we've been told is, if possible, have EVERYTHING registered in one state. We head to S. Dakota next weekend to sign up with Americas Mailbox, and get everything going, so we'll find out the answers to any questions we still have.
We chose them because they are also in one of the counties that doesnt have the wheel tax. Every penny saved is a bonus in our book. So far, theyve been great to work with and get info from. Theres also alot of info to gather if you just google "claiming a home state".