As I’m prepping to leave, I’ve just found out there’s a new form necessary for processing your Anmeldung or Abmeldung:  The Wohnungsgeberbestätigung.  As of November 2015, when you go to register your residence or your move, you are now required to provide a form from your landlord confirming that you are moving in or out.  You should go to your local authority’s site to download it, as it seems to vary from place to place.