I've often found that talking too much is what gets you assignments in meetings. With a large enough group, it is best to the quietest person in the boss' sphere of influence. Close to the boss, they tend to task the people whose comments brought the "good idea fairy" to come to the room in the first place.
For random, menial tasks, the boss looks around the immediate sphere to see who is hanging out in the wings.
Thus close and quiet is the way to go to avoid the good idea fairy taking a crap on you.