Does roundcube support webmail open to the public i.e. hotmail/gmail?
In which a user registers with a website and he/she obtains an account.
there are no registration functions in the RC core since it is impossible to make a single solution which will work with every setup but have a look at MyRoundCube © www.roland-liebl.de (http://dl.roland-liebl.de/MyRoundCube/) (demo: mail4us.net :: Welcome to mail4us.net (http://mail4us.net/)) this is a mod'd version of RC which allows registration and many other things but i am not sure what backend the registration requires.
The backend is hMailserver 5.1.