Trade it in for an even more expensive car. Continue to stay in debt.
Do NOT keep the car for 10+ years.
Do NOT keep making the monthly payment into your "next car" savings account.
Do NOT pay cash for your next car.
Do NOT advice your younger friends to buy only as expensive of a first car, as they can pay off within 12 months.
[/sarcasm off]
The State keeps your Title of Ownership, since the States will always own you car, house, etc. The car dealership always sends the Title of Ownership to the State, and the State will not EVER release the Title of Ownership to a Citizen, only to another State. The State will, however, send you a Deed of Trust, to keep track of who is responsible for paying the annual taxes, however. But yes, the bank should inform the State that they are no longer the leanowner, and the State will send you some kind of Title of Possession or Deed of Trust. Each state is slightly different. In theory, you should not have to do anything, but paperwork glitches happen all the time. As long as you pay your property taxes and license taxes, the paperwork can stay "lost in the mail" for months and noone will care, but hopefully you get your copy within a month (or two at max) of your final payment. Depending on which State(s) you live in and travel in, you may or maynot have to keep a copy of or the original Title in your car at all times, to produce when the cops demand to see your papers. "Show me your Papers!"