The iPlayer download services uses a system called "Kontiki" (see
http://en.wikipedia.org/wiki/Kontiki ) to manage the downloads. It's the same system as Sky's Anytime and Channel 4's 4od.
By default, the system
does carry on sharing when you quit the client, although iplayer gives the option of not sharing. 4od does not, and, AFAIK, Sky anytime does not either.
The sharing is done by a Windows service called Kservice.exe, and this can be shut down through either computer management, or by opening a command window, and type "net stop kservice".