I looked into this awhile back.
The video of an HHO generator was really impressive, so many bubbles coming out of that thing! Back in high school chemistry when we split water it was really slow.
So I calculated the amount of air that passes through an engine during operation, and compared that to the liters / second of HHO being generated, and that's when I left it be. The HHO is negligible. You might as well just fart into your intake.
If I was really smart, I'd calculate the energy required to split a water molecule, and calculate the energy it gives up when you burn the hydrogen and recombine it with the oxygen, but I can guarantee you will lose energy in the process, you won't get back what you use.
I'm an EE, not a Chem E, but there ARE guys that know how to calculate that, and it has been looked at, no doubt. If there were a way to make it come out > 100%, they would have been doing it a long time ago!
The people using them on their vehicles, and getting dramatic mpg increases, are doing a number of other things along with it such as monkeying with the MAP sensor. That's nothing new.
You can do things to lean out your engine and boost your gas mileage but your valves will burn up prematurely.
File this one under, "there ain't no free lunch".