Expired Private Leagues

I have 3 old expired private leagues on my character select screen. Are they supposed to just sit there forever?

If I join a 4th private league, will the oldest one drop out and get replaced by the new one? (There isn't room for more than 3 on the character select screen)

OK apparently the 4th private league gets added to the bottom and a scrollbar appears, but the old useless leagues are still listed above. seems dumb, are these old ones going to hang around forever...?

tl;dr Private Leagues behave like the current league.

If you don't continue to fund them, they sit idle till the current league (Betrayal) ends and will be automatically migrated (contents like tabs contents and Atlas) to standard.

There is no option to migrate it per hand to standard or the current league if it is not funded (just sits idle). The only options you have is to put a minimum amount of money in it and then use the "Migrate All" Option with the character that sits in the private league. The private league contents (tabs contents, Atlas progress, etc) will then be transferred to the current league (Betrayal).

But you can still play the private league because you have funded it, by creating a new character. But you used the "Migrate All" option, you will start from fresh.