When you move out of Germany, you must deregister your address. This is called the Abmeldung.
When you deregister, you get a deregistration certificate (Abmeldebescheinigung). You can use this certificate to stop paying TV tax, cancel your contracts, and stop paying for health insurance.
In Berlin, you can do your Abmeldung by post, by email, or in person at the Bürgeramt. You can also pay someone to do it for you.