Does the insurance company own the car after it is totaled?

You can put in an offer to buy the written off vehicle from the Insurers if you want to repair it yourself. A write off is beyond economical repair, meaning it costs more than the car is worth to fix it. It doesn't mean it cannot be repaired. There are different categories of scrapped vehicles, D, C etc. The Insurers sell the written off cars on to scrap merchants or motor traders to recoup their losses. You are perfectly entitled to buy the car back yourself for a nominal price. If the Insurers are settling your claim and giving you a settlement to get a replacement car, the damged vehicle does in effect belong to the Insurers. Hope this helps, I worked in insurance for 10 years.