LimeWire will remember the files you were downloading, but it's rather likely the sources have expired until you restart, so many downloads won't resume unless you do another search for them. Don't kill you downloads, however. LimeWire will resume from all sources you find automatically.

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Morgens ess ich Cornflakes und abends ess ich Brot
Und wenn ich lang genug gelebt hab, dann sterb ich und bin tot

--Fischmob