Roscoe,
When a car had been declared as a write-off by your insurance company, they will offer you a "fair price" for the current value of your vehicle following an assessment. Once you have accepted their offer, the car becomes the property of the insurer. They normally ask you to send your Vehicle Registration Certificate (Log Book) along with other relevant documents following the settlement of your claim. All personal belongings should be removed and keys supplied. The insurance company will then arrange for the car to be scrapped. So to answer your question, the insurance company normally gets ownership of the car unless you have arranged another agreement with them.
