Have you looked at the profile.php page? For instance, if you edit the password, you go to do=editpassword. The action then is do=updatepassword. At the end of the code for do=updatepassword is the redirect (example):
PHP Code:
eval(print_standard_redirect('redirect_updatethanks'));
It is similar for all of the (do=editprofile has the action do=updateprofile, editoptions goes to updateoptions, etc.)