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Does not matter where its "being refined" Energy In will always be more than energy out. Period. Until the laws of physics and chemistry as we know them change this is not a point of discussion.
It also does not matter if the H2 is being produced in the car. It all comes down to HOW MUCH does it cost. If you want to produce the H2 from the engine itself well there is a lot going on here. Sure the power has to ultimately come from the engine so this would seem to be a lose lose scenario but it depends I do not know enough about it to say yes or no. MY GUT tells me that if your using electrolysis that once you have enough amps from a battery to produce enough hydrogen to run a car you already have enough amps to go twice as far as an electric car IE no point.
Now if there is a chemical way to release H2 IE you fill a tank with water and "add" a catalyst well the question is NOT which is more efficient (remember thats irrelevant to me and SHOULD be irrelevant to you) the question is which is cheaper.
IE is enough catalyst to go 300 miles cheaper than the equivalent amount of gasoline.
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