There is a process for getting an "abandoned vehicle" title in Tennessee. I'm currently doing that with a Suzuki motorcycle that was given to me without paperwork to get the Nashville codes department off a friend's back. It involves getting a VIN number verification from a law enforcement facility and a value appraisal from a licensed dealer, and some paperwork submitted through your local county clerk's office, but it's a pretty straightforward process. On low-value vehicles and antiques, it doesn't even involve posting a bond equal to the appraised value.
Jerry