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The League division is populated by group/tourney members. The main purpose of League is to be the home for user-created tournaments, but one-off matches may also be played (although once a team signs up for a particular league, the tournament organisers may no longer permit this).
Head for the Groups page and you will find many tournaments looking to recruit League teams. Each of these user-run tournaments has its own rules and system for arranging games - read individual group pages to find out the details in each case.
If you are just looking for a one-off game with a League team, are in the #fumbblleague IRC channel and want to play a game with one of your League teams, make sure your chat name is the same as your FUMBBL coach name ( type /nick yourcoachname ) and then type bb lfg to display your teams in the channel. You can also open the Gamefinder page, and list your teams there - seek out likely-looking opponents on IRC.
For Ranking purposes, K=0 in this division. In other words, it is not ranked at all.