In about half the states, the lienholder is given physical possession of the title until the loan is paid off. In the other half, the customer has physical possession. Even in those states where the lienholder has possession, the customer is typically the "owner" of the vehicle. In rare cases - usually in very small dealerships or with "buy here, pay here, the dealer or finance company may retain "ownership." I'm not sure about all states, but in least in some, "ownership" carries insurance obligations which the finance companies don't want to assume.