We have an answer!!!

Thanks to Joe, I know what I have to do to solve my conundrum!

He kindly left a comment with really handy links!!!

As I'm staying for more then 3 months it is compulsory for me to register my address

There are offices all over Koln (it is a large city!)

The form dosent seam that long or complicated but I dont understand it! Must look for stuff on it in English!