They'll never (in my lifetime at least) be fully autonomous like I am, because then they would be responsible for accidents and by that time we'd have to have courts and prisons for robots. They'll be autonomous at the "do what my owner says at a supervisory level". I expect what many cars will do when they're fine-detail autonomous is "go out and earn me money". It'll be the next BuyToLet. Wealthy people will buy self-driving cars that less wealthy people will rent. The cars won't need parking space - it'll be cheaper to drive around or 'hide' during quiet times. They'll book their own servicing and valet visits.
The cars won't be our overlords; the wealthy people who own our transport and accommodation will be. 'Carlords' competing with each other for our transport coin can only be a good thing - I can't see how they'll be able to monopolise supply like they have with accommodation.