It will change from insurance to product liability.
No more than it is at present. The person or company that will have to pay (and therefore will need insurance) will be the person or company that was to blame for the accident. In most cases the blame will *not* be with the self-driving car manufacturer. If the automatic system failed to avoid an accident that it should have been able to avoid, the cause of the failure will determine who pays, which might be the manufacturer if it was a design fault, but may well be the owner of the car who failed to maintain it properly, or a garage that failed to service or repair it correctly. If your wheel comes off and causes a fatal accident, it is not Dunlop or the car manufacturer who is held to blame *unless* there was a design or manufacturing fault in the wheel or fasteners. What we may well find is that the number of accidents caused by owners/drivers fall to such a low level that 3rd party insurance will no longer be mandatory - any more than pedestrians or cyclists have to have insurance even though they sometimes cause expensive accidents. It may be of interest to know that 3rd party insurance is not mandatory for private pilots in the UK for a similar reason.