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BT Sport doesn't have any device registration requirements - you can use as many different devices as you want, as long as not more than 2 of them are watching live content at the same time.
BT TV unfortunately is a lot more restricted, due to rules imposed on us by the content providers. You can therefore only have 2 named devices at any one time (or 4 if you have BT TV App Extra).
It has been known for accounts to become stuck, with device slots not being correctly freed up. Send me a DM by clicking here and let me know the BT ID you're logged into the app with. I'll check the state of your devices and free them up if needed.