POP "leave on server " simply downloads the all mail in the mailbox (headers/messages/attachments) that hasn't previously been downloaded by that client and then leaves any messages on the server that have been downloaded within the "leave on server" time period deleting mail downloaded prior to that time span. good for being able to access read and write (if not send) mail off line, slow particularly on dial up.

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I'm pretty sure IMAP allows you to ONLY download the headers so you can then download the message body when you want to read it. good for mobile devices or dialup/satellite access but can't read mail that hasn't been already read (or selected to download) when offline

Yup, you're correct.  Good point.
Andrew