We have more than ten follow-up forms from the registration. Following registration, a list of cases appears in the case list, which will be followed upon. In this situation, how to automatically close or vanish after data are collected in the same follow-up form case list.
It sounds like after registration you want cases to only appear once for each of 10 individual followup forms?
I'd recommend setting a unique property on each case after each of the 10 forms is completed. Depending on your app structure, you could then either filter out Cases from the Case List associated with each form (if you are choosing forms-then-cases) or filter out Forms which have already been completed for each case (if you are choosing cases then forms).
In order to remove cases which have received all 10 followups, you'll want to make sure that either each form closes the case if it has now received all 10 servies, or use something like an auto close rule to closes cases which have received all 10 services. Otherwise they'll remain on phones even though they aren't visible, which could cause performance problems.