The few I have done have been like a multi viewpoint story, with each person writing from the point of view of their character or characters, with a couple of free characters that everyone can write thrown in. For example: I'd write, "Character A accidentily runs into character B and shoots lightning at him" incredibly eloquently, and Character B's writer would jump in to write, "Fotrunately B had chosen this day to wear his rubber suit"
I'm simplifying it of course, the one's I've done haven't been pedantic at all. Just don't do anything drastic to anyone else's characters (which is why my example is a bad one), unless you discuss it with them first in a personal message.
I'm not saying we have to do it this way, it's just the way I've done it before.
There's also usually some simple rules/laws for the created universe, and general guidelines for character creation. For example, although I really would love to be myself, the shard of brain activity, such a character probably wouldn't be fun to write/read about after the first few amusing view points, because not much is at stake, I wouldn't have much to do with the other characters, and it takes a certain person to be a 'god' character and not ruin it for the rest of the players.