How do I install iPadOS 13 on my iPad?

Use a computer or the Software Update function in Settings. If you encounter a specific issue other than the one listed below, describe it in this thread.

An unit on 12.5.7, or one which shows 12.5.7 as available, isn't capable of 13 or above.

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For the original iPad Air, the iPad mini 2, and the iPad mini 3, iOS 12 is the end of the line. No update to iPadOS 13 is, or will be, available for these iPads.