This has been asked a few times. I am not sure of the actually rules, but I have a few observations regarding with a regent is away/unavailable from/for the domain:
1. Even when a domain is leaderless, it may perform 1 REGENT action (in the past, RP influence was not neccessarily allowed).
2. The LT continues to provide a BONUS action (as long as the LT is available).
3. The regent may perform 3 character actions/turn.
From a more theoretical sense (since I haven't ever really done this before), if you can secure stable supply lines, maintain some resources in your court (able-assistance, LT, etc), then you likely can have all your 'normal actions', with the following caveats: you will likely need to expend 1 Wage War and 1 Adventure action (for regent). So you are really talking about 1 or 2 actions for your normal court.
I actually intend on temporarily moving my court (which is kinda what happened in the Crusades).
Bjorn??? Jon??