I recently had my car written off, not my fault. They paid me out. Market value of my car was set at 10,300 by their insurance company. They got quotes on salvage price which was $1,300.
Their insurance paid me $9000.
Leaving me with the car and contact details of a wrecker which i had to ring and they took my car away, and paid me the remaining $1300. I think you legally own the car after they pay you out the amount less salvage, leaving you with choice of selling it to the wrecker they choose or you can keep your car.
Their insurance company was RACV. SO it may be different with just cars.
Cant be bothered reading back over that so i hope it makes sense.
Cheers,
Paradizzle.