German plates are 'personal' to the individual. When you change cars you put your 'personal' plate on to the new car. The first letters (before the two dots} refer to the city/town where you live - M=Munich, S=Stuttgart, COC=Cochem etc. If you move from say Munich to Stuttgart you have to register you car and get a new number and set of plates issued. It is also possible to register a car or motorcycle for say 6 months of the year at a reduced rate. Useful for people who only use a motorcycle, soft-top or classic car during the summer months. This is also indicated on the number plates. All new plates issued are EU type plates. There are no cases of mis-spaced letters and numbers etc because the local government department 'issues' the plates and it is illegal for anyone else to make up number plates. There are still some personal plates about. The best one I've seen was on a Porsche 911 near Stuttgart - S:EX 69!!
Germans can collect their new car direct from the Audi factory if the want to. If you visit the Audi Forum at the factory in Ingolstadt, you will see people arriving to collect the new car with a set of number plates under their arms. They hand these in at reception and then go on a factory tour and then have some lunch by which time their plates have been fitted to their new car and it is in the collection area at the specified time wait for them. Audi show them round their new car, they have the photo taken with it and then drive it home. Makes for a great day.