For a used vehicle purchased from an out-of-state dealer, you will need to provide an out-of-state title certificate or transferrable registration transferred to the dealer, OR the dealer’s bill of sale that transfers ownership to you
so will I need to register if I move to NY full time?
Yes,  you must register your vehicle here within 30 days of becoming a resident
If my car had been purchased new from a New Jersey dealership what would I need as proof of ownership?