While you make it, it's yours
An album you make for someone else is yours until they have it: you run it and it uses your storage.
If they're on your tree
Invite them from their card. The albums you made for them are ticked; when they join, those become theirs — their storage, and they run them. Tick Leave these albums once they've joined if they'd rather have them all to themselves.
Anyone else: give it
Studio → Settings → Give this album to someone: add a note and their email. When they accept, it's theirs. You stay an admin they can remove — or choose Give it away completely and you leave when they accept.
A surprise
Set a scheduled reveal first. Then the gift can wait for that moment: we email it at the reveal, so they don't see it before. Move the reveal and the gift moves with it.
Sharing the running of it
To run an album together instead, make them an Admin in Studio → People.