A couple points on HHO theory

The amount (in liters) of HHO gas generated by those that you add onto a vehicle and numbers I have read regarding the BTU value of the hydrogen generated, is a fraction of the BTU content in gasoline.     Here is my theory on what injecting the hydrogen into the engine is doing.

Because of its pure state, HHO is lighting faster and burning hotter inside the engine cylinder than atomized gasoline.   The atomized gasoline in the cylinder is more completely (efficiently) burned because of the hydrogen in the cylinder.  So the hydrogen effect is actually very little due to displacement of gasoline used, but rather has a catalyst effect that dramatically improves the burning of the gasoline.  

The reduction of tailpipe emmissions when hydrogen is added to the combusion is documented and not an issue of contention.    The issue of contention is "free energy" and the cost ( engine performance cost) of generating electricity in the amount from the alternator to generate enough HHO btu to have any effect.