I think these are two very different questions:
- What’s the hypothetical maximum (allowing nonsensical games where both players just conspire to inflate the disparity)?
- What’s the largest disparity that you’ve seen in a “normal”, sensible game (where both players, preferably stronger ones, are playing well and just trying to win)?
The first is a mathematical problem, while the second requires examining actual games. I think @Skurj means to ask about the second question, which I am quite curious about as well. I hope that people provide some examples to respond to the second question.
The same could happen in a Japanese rules game.
If you consider Japanese rules and let white win by komi, then white does not need to put any stones on the board. Black can put 359 living stones on the board, with two eyes giving only two points of territory.
Thus, the largest (uncontroversial) disparity seems to be 359.
We could consider whether 360 is possible, but I think that would involve a rules debate to resolve. If black has 360 stones on the board (all but one point occupied), and then both players pass, are black’s stones alive?
The Japanese rules have an interesting way of defining “alive”:
[Article 7.1] Stones are said to be “alive” if they cannot be captured by the opponent, or if capturing them would enable a new stone to be played that the opponent could not capture.
Even though a 360-stone group with just one eye could be immediately captured, doing so would leave an almost wide-open board, where black could clearly play additional stones that would live. So, I believe that a 360-stone group, if both players pass and agree to end the game, would be considered alive. White would have no interest in capturing that group to continue the game, since komi already gives white the win.
Thus, if you accept my line of reasoning, then 360 seems to be the maximum disparity.
Reconsidering the definition of “disparity”, if we simply count all stones present after both players pass, but before we remove any “dead” stones, then clearly, the above rules debate is not necessary, and we could say that 360 is the maximum disparity, even if we were to argue that a 360-stone group is ultimately dead.