I will do very little actual leading of you guys (hopefully) once you're all entered, so if you happen to have a character in each of two parties that cross paths, and those parties decide the other ones are a threat, then I suppose you'll be forced to fight yourself. :P
On that note, a little more about how this game will work and it's system of 'guidance': I'll have the map drawn out and all of your locations will be tracked by me, but you guys won't see the map naturally, however, the game will be sort of playing out as kind of... D&D game, but not really. Gallie will be toying with his people, and watching all their moves and choices, so - like in a game of D&D - he may decide to reward a party (or loner, who will from now one also be referred to as parties) with items they find, which could include a glimpse at a map.
Also, as I mentioned before, the Labyrinth isn't your everyday maze that's just a bunch of walls at right angles while you look for an exit. It's an entire plane of existence developed as a toybox of adventure full of puzzles, monsters, towns and cities, worldly elements from all of your worlds (hence the need for links to your RPs), to worlds you've never heard of in or out of game, all in one seamless existence... although 'seamless' here is used at the discretion of a psychotic old-ass arcane. Some parts, however, will actually be walls-at-right-angle mazes. In fact, no matter where you are, you'll probably always technically be between two walls so you're always technically on a definite path.
That also reminds me, since there will be tons of NPCs around (which aren't actually NON-player characters, 'cause I'M playing them... so maybe TPC for Timmy-played character! :D!) for you to be interacting with (seeing as it's a role-playing game and all), there will also be items and such to discover and possible ways to make yourself more powerful. This game won't be flattened out where you stay as strong as you are when you enter, but it'll all come down to your RP decisions.