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I have registered and re-registered my Kindle for PC many times without it being listed as multiple devices. What's more, if you re-register it on the same computer and the files are still in the Kindle Content directory you can still open them after you re-register. If it's a new computer, or if the files are no longer in the Kindle Content directory, then you need to redownload. So it depends on the circumstances. I did have to redownload when I switched computers!
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