How big does the gap have to be?

[sm0ky2]

No current means no arcing. You can go as high of voltage as you like.

pure distilled Water will break down at around +/- 90Kv if sufficient charge capacity is maintained.
resistance will drop to 0, current increases infinitely until the charge is dissapated, or the water is completely consumed. This can occur across great distances of water, up to several feet.
However, this is not the desired result, as much of the liberated gasses will fuse with nitrogen in the air forming NH3  and 'ozone' (O3),  very similar to what happens when lightning strikes water. 

Water with electrolyte will break down at less voltage.    Ideally you want to have 'some resistance'
so HV electrolosys is not the way to go if you want to produce useable hydrogen gas.

Also,. resistance [builds up] as voltage increases up to the breakdown point, making the process less efficient at higher voltages.  Ideally, electrolosys should be performed between 3v-300v
i have seen it done with as little as 1.5v (AA battery w/ pencil leads experiment)
personally i prefer 12-24v from my experience with electrolyzers.

Variable Gap size is the most convenient way of adjusting the current if you plan to use pure water.
  measure it with no current flowing, by connecting an Ohm-meter to the circuit then decreasing gap size until the desired resistance is reached.

Also   -- i've been steering away from "plates",  as i have found that Helix-Coils perform much better
  and they respond more quickly, allowing for higher frequencies