There is a limit of 10 devices that can be associated with an Apple ID. The questioner is asking how to permanently remove a particular device from that AppleID and associate a new one. Kappy you are not understanding the question. Unplugging does not permanently dissociate the device from the AppleID. I need this answer also. Please help.
De-authorize it. Or check the instructions given in the Learn about link at the top of this topic. Also check the links below the heading "More Like This" on the right side of the page.
Authorization and Deauthorization
In iTunes you use the Authorize This Computer or De-authorize This Computer option under the Store menu in iTunes' menubar. For Windows use the ALT-S keys to access it.
More On De-authorizing Computers (contributed by user John Galt)
You can de-authorize individual computers, but only by using those computers. The only other option is to "de-authorize all" from your iTunes account.
1. Open iTunes on a computer
2. From the Store menu, select "View my Account..."
3. Sign in with your Apple ID and password.
4. Under "Computer Authorizations" select "De-authorize All".
5. Authorize each computer you still have, as you may require.
You may only do this once per year.
After you "de-authorize all" your authorized computers, re-authorize each one as required.
If you have de-authorized all computers and need to do it again, but your year has not elapsed, then contact: Apple - Support - iTunes - Contact Us.
The problem is that the help article here
says to select 'manage devices' but that option is NOT present when one logs into iTunes. It seems the help documentation is out of sync with how the newer iTunes works.
I know - gasp! shocking! Documentation that is outdated! - trouble is, Apple is a huge company and shouldn't let this happen.