The competitors supply their own cook pots, since some stoves are particular about that. The cook pot has to be strong enough that a competitor can stand on it. Otherwise, somebody will show up with a cook pot made out of aluminum foil.
The judge supplies the water to be boiled. The water will be in a jug at ambient air temperature, whatever that is, and the judge places exactly 16 ounces of it into each of several smaller bottles. That way, the water should all be the same. Each competitor picks one of those smaller bottles of water and applies every drop of it to his or her cook pot. That way, the competitors can't get an advantage out of the water.
Competition grade wood? The mind boggles. If there is no kindling involved, the wood had better be pretty small in diameter, perhaps 1/4" pine dowel rod from a store. One large pinch of firestarter from the judge might level the playing field there.
It will be tough to decide when the water is exactly boiling. You can't put a thermometer in there, because that would interfere with the lid. You might have to go by sight, but that is pretty subjective. You might have to have instrumentation.