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The quick answer is that it depends on HOW you set up the POP account settings. One of the KEY settings for any POP account is to set something called "Leave messages on server". This will be called different things in different places, but the idea is the same. POP usually downloads the emails from the remote server to a local place and removes the entry from the server unless you explicitly tell it NOT to do so.
The downside of using POP in multiple places is keeping everything up to date. If you don't set this flag to keep the messages on the server, then the first device that gets to the server gets the email and no other device does. But if you set the flag, then every device picks up the same email and marks it new and so on.
IMAP is the better way of dealing with email in general.
Anyway, bottomline if set up your POP account and forgot/neglected to set the flag to save the messages on the server, you might have just lost all of your email..