How to de-authorize devices linked to your iTunes account
Authorizing an iPhone, iPod, iPad, Mac, or PC on your iTunes account means you can uses it buy new apps, music, movies, TV Shows, and iBooks, re-download previous purchases, access iTunes Match and more. Because of licensing agreements, you can only have 10 devices total, and a maximum of 5 computers total, authorized on your iTunes account at any one time. Once you hit 10, you'll have to remove an old device to add a new one. If you give away, sell, or lose a device, you might want to remove it as well. Luckily the process it fairly straightforward and can be done right from iTunes on any Mac or PC.
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