Well we already have assisted parking!
I think in the case of impending accidents...fail-safe braking etc. kicks in and control is given back to the "driver"
So the driver is probably responsible.
But what is interesting is how a "smart" car that is familiar with a route could interact with a driver given "permission" not to concentrate.
Ten years. That's my prediction. In another ten years after that, self-driving cars will be more common than cars without the capability.
I think that the technology will start with the assisted parking, lane holding and adaptive cruise control systems that we're seeing now in high end card. It will filter down and little by little work toward full autonomous driving. In half a decade, most new cars will have a pretty aggressive adaptive cruise control as well as emergency accident avoidance assist.
A lot of people seem to think that the computer assist would be best in normal driving activities, with a human driver being superior in an emergency. That may be the case for a skilled and well trained rally driver, but not for most of us.
Remember, the automakers move a bit more slowly than CE companies. I think in 10 years we will start to see this in production cars, but it's probably 20 years before cars that can drive autonomously are more common than those that cannot.
I think it will move faster because self-drive will become compelling when coupled to other transitions and the current vehicle manufacturers may be displaced.
The game changing package will be self drive + electric vehicle + radical new layout (e.g. no steering wheel) + new business model. Instead of owning cars we will pay a fee to be able to summon a car on demand.