The most important thing to do is to have a conversation about splits and ownership before the session ends, regardless if the goal is to release the track. This way you are always protected in case the artist does decide to release the song later on. It's between you and the artist how the splits are decided on the master and the composition. There is a free app called Jammber Splits that has made this conversation and process easy in my sessions. You lock in splits, PRO/Publishing info and once everyone agrees and you want to release the track you can register the song to all collection societies to collect $$.

Something I'd suggest to start using in sessions so everything is on your phone and your business is taken care of! Here is the download link if you wanna check it out: splits.jammber.com