It can be more complicated than that if you want it to be. ☺ Normally, though, factotum is started once when a user boots a terminal, and that one instance is used throughout. on a cpu server, it's slightly more complicated, but not much: there's one started for the hostowner, and each user gets their own when they call in. See the calls to auth/factotum in the default profile, typically set up by /sys/lib/newuser.
Anthony