I don't use Character Trees, but I love this idea and may adopt it for our games. So if anyone else has stories like this, I'd be interested in hearing about them.
I run a campaign that utilizes a Character Stable, albeit in 3.5. I'll try to keep my response edition-neutral. In my campaign, each player makes up to five characters. At any point in time a player can place one of their characters in semi-retirement or retirement. Semi-retired characters are temporarily transferred to me as NPCs, with the intent that someday they will transfer back to the player as a PC. I will make small decisions for the character, but typically nothing major. There has been a handful of exceptions. Retired characters become full-fledged NPCs that I can use as I see fit.
My campaign focuses on a specific region; in this case, Law's Forge, the Shield Lands, in the World of Greyhawk. Law's Forge serves as the base of operations for the characters. Each character must have a reason to be in Law's Forge. I like having a base of operations as it makes interaction between the PCs feel more natural.
Adventures are typically player-driven. That is, at the end of each session, the players discuss what they want to do the following session with their PCs. That's what I prep. (I'm lucky that I have five players who are all self-motivated.) Adventures typically run one-to-two sessions, and always begin and end with the PCs in Law's Forge. Again, having a base of operations helps facilitate a smooth transfer from adventure to adventure, and PC to PC. Sometimes the on-going narrative does not allow this. In these instances, I prefer to just keep running the adventure, with no PC swapping, until they reach Law's Forge.
Unlike [MENTION=6787650]emdw45[/MENTION], I do allow players to have their PCs interact on-screen and off. I will allow a player to run more than one PC simultaneously. These situations are rare, but do arise from time-to-time.
Each PC has his/her own XP total and levels up independently of the other PCs. New PCs are brought in at the same XP total as the lowest XP total of all the PCs. If I ever switch to E6 I'll start each new PC at 0 XP.
Currently, my five players have twenty-three PCs amongst them. Last session ended with five of the PCs securing an alliance with the Wolf Nomads and trekking back to Law's Forge. The next session will be the start of a simultaneous assault on three of the Hierarchs of the Horned Society. The players have split the PCs into three parties of five, each tasked with assaulting one of the Hierarchs. The remaining eight PCs are hanging back in Law's Forge to defend the town should the Hierarchs retaliate.