Yep, duh, the motor has a battery so it's an electric auto.

Arf we go round the mulberry bush the mulberry bush until pop goes the weasel.

You're smoking or snorting again martinduck.

Oh just the fact that there is no electric motor in the vehicles powered this way.

There are no vehicles powered this way at all, but I haven't supposed any electric motor. You're still burning gasoline to drive an electric generator to electrolyze water into hydrogen and oxygen so you can then burn the hydrogen back into water. You're still converting the energy from gasoline into electricity before converting it into hydrogen. You could just as easily use this electricity to drive an electric motor, which is what GM proposes to do with the Volt. I have no idea why inserting hydrogen into the thermodynamic equation helps anything.

Oh just the fact that there is no electric motor in the vehicles powered this way

Which would seem to be me to be a huuuuuuuuge miss.

It is separated from the water by electric power from a battery, yes.

Right. So a car driven by hydrogen generated this way essentially is an electric car. What have I misunderstood?

So, we see hydrogen in abundance, easily captured and produced.

Hydrogen and Oxygen gases produced from water through electrolysis contain more energy than Hydrogen and Oxygen bound in water molecules; therefore, energy must be added to the water to produce the H and O gases. Then burning the gases liberates this energy by recombining the H and O into water. The free hydrogen is not the source of the energy yielded by burning it. The electrolysis is the source of this energy.

It's like a satellite orbiting the Earth. To boost the satellite into a higher orbit, a rocket must expend energy. That's like the energy freeing the Hydrogen from the Oxygen molecule. Unlike classical Gravity, the Electromagnetic force binding H to O in water can draw free H back into a water molecule by radiating this energy. That's the burning H and O to yield water.

Now we just need to see technical advancement of the operation to where it becomes viable enough to replace fossil fuels in internal combustion engines.

Again, Hydrogen is not an energy source. It's an energy storage medium. Conventional internal combustion engines can't use it, so we need new engines. Conventional gas pipelines can't transport it, so we need an entirely new gas distribution infrastructure, and we need entirely new refueling stations. Also, the energy density, by volume, of Hydrogen is much less than the energy density of gasoline, even if the Hydrogen is in liquid form (which must be supercooled), so a Hydrogen car requires a much larger storage tank to achieve the same range.

I don't pretend to know what new technology ultimately will replace the gasoline driven internal combustion engine, but hybrid electric cars certainly seem the best bet in the intermediate term. They're certainly where the serious bets are placed now.