Hydrogen can be released from water through an electronic process. However, the process utilizes more energy than you could get back by burning the hydrogen. Chemically, you have H20, which you can split into H2 and O. HHO is not a valid molecular combination. In water, you can chemically make H+ and OH-, but only by combining the hydrogens with some other chemical to make an acid or a base. H2SO4, for instance is Hydrochloric Acid, which is used in lead acid batteries. You can't make HHO, because hydrogen in a gas form becomes H2(not HH, which would spontaneously combine into H2), and if you have H2+O and a heat source, you get H2O.
Why does it take more energy to split H20 into H2 and O than you get if you burn H20? Because H20 is a very stable molecule. Oxygen needs two electrons, and hydrogen has an extra, so you get a strong covalent bond where the hydrogens share their electrons with the oxygen to make a stable molecule. Breaking this bond requires energy. Mixing H2 and O and applying fire creates H2O, and releases the energy that you put into separating them in the first place. Of course, some of this energy is lost to entropy in the separation, and some more is lost in the recombining. So the net effect is that you put in some amount of energy to separate the atoms, but if you burn the product, you never can get out the amount of energy you put into it in the first place, so it would be more efficient to just use the energy you are using to separate the water molecules to drive the car.
Note also that Oxygen in a gas combines spontaneously into O2 and O3(ozone). So, if for some reason you mixed your liberated electrolyzed gases you'd be more likely to get H2 O2 and O3, a very explosive mixture that with a tiny amount of heat or spark would create a nifty little explosion resulting in H2O and heat being released. There really is no safe way to store mixed hydrogen and oxygen. If there were, the Hindenburg would still be sitting in a museum gathering dust somewhere.
Dont mean to nitpick, but H2SO4 is Sulfuric acid.
Hydrochloric is HCl
My battery uses sulfuric acid, which is what H2S04 is in my science book. I don't think you'd have any lead left if you put hydrocloric acid in your battery. you might notice a dangerous cloud though.