"A: On Windows, Linux, all Unixes, and Mac OSX, LimeWire's default closing behavior is to remain open until all current uploads and downloads are completed. This means that LimeWire will not allow any new uploads or downloads, but it will automatically stay open for current transfers to complete before shutting down. You can change this behavior in the Tools>>Options window under "Shutdown.""

The above is from the Limewire FAQ.

There are a number of ways to log off , the friendliest way is to choose File > disconnect in Mac ..perhaps a little different in Windows. Limewire will continue to download and upload from hosts it is connected to and this can in practice sometimes take hours! Otherwise just Close Limewire. In Mac this is not possible unless the monitor window and the download window are free of up/downloads, although in Windows I believe this is not necessary. I find that the shutdown on my mac system behaves different from Windows, hence my inability to give you an exact procedure.

Take a good look at the user guide and FAQ linked below.
I hope this helps.

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