To manually remove the authenticator from an account from the Battle.net site, you do not need to have the serial number to the authenticator.
However, you do need to input 2 consecutive authenticator keys. That protection makes this type of attack nearly impossible to carry out. Not impossible, just nearly so.
In order to remove the authenticator from a Battle.net account when you no longer have access to the authenticator is a bit more problematic. I have had 2 iPhones crap out taking the authenticator program with it, and since the authenticator program uses the serial number of the phone itself as a portion of the key generation algorithm, this means that a restore to a new iPhone does not result in the correct key being produced. I have had to fax in a form to Blizzard with specific account information and also a photocopy of my government issued ID card (for me a driver's license) and they then removed the authenticator from the account.
Just FYI.
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