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How do I bring up the history of what has been downloaded and deleted?

As far as I know this is not possible. If you make a Limewire search and a file shows up with a green tick, this means you have downloaded it. If you then delete it I am not sure it will still show the green tick. At any rate, after a while if you or the other host has made any minor changes to the file name, it probably will not show up with the tick.

This only applies to specific searches, and does not really answer your question which is afaik You cannot. If you have a particular reason for asking, tell us what is and we'll try to help:)

Files deleted, remain on your computer, but may at any time be overwritten. If they have not been overwritten they can be located using specialized software. linked in this post. Just a guess that that might be why you are asking:)
http://gnutellaforums.com/showthread.php?t=49851