My experience is that "The Celebrated Taper System" consists of a barrel having the choke at the muzzle like any other choke system. Where it differs from the "Conventional System" is it lacks a parallel at the extreme muzzle end of the choke but rather is a tapered cone for its entirety. The full chokes on my Lefevers which are bored on the taper system measure in the vicinity of 4" long which is longer than the cone & parallel combined on most conventional chokes.
My very early Lefevers also have larger than standard bores, presumably for the use of oversize wads in all brass shells.
The British Wildfowlers Association as I understand it developed what they called a chamberless gun for use with the thin brass shells. The chamber cone extended into tghe bore itself with no secondary forcing cone at all. The bores were vastly oversize & did require the use of special wadding.