Water induction into jet engines was a common technique to product greater thrust ( AV-8B's (Harriers) do it actually). The water is sprayed as a vapour into the ingested air stream, reducing the temperature of the inlet air, increasing density and hence producing more thrust. The water expands into steam during the combustion cycle, so no residual water. The problem with this for aircraft is you firstly have to carry this extra weight off the ground, and the performance increase is negated by the additional weight ( of both the water and the ingestion system).
This is a very different concept though to hydrolising water to produce hydrogen, and combusting the hydrogen and oxygen. The water atom is not split during the combustion cycle.
Fuel has one of the highest calorific values of any fluid that we currently have access to. (calorific value is the amount of thermal energy that can be extracted from a volume of the fluid ). This makes it a very efficient energy source to carrry and use. However, it is a combustion cycle that is used to extract this energy, and not atomic division.
Interesting stuff though.
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