Do i loose height when having a coxarthrosis on one side? i mean is a cartilage so thick, that if it is nearly gone, i loose some inches? thanks

Yes but mechanics: It may be narrowed on one side but not the other and if your height is measured with you standing straight it may make a minimal amount of difference

A very small amount: I assume you are speaking of hip arthritis. If both hips have complete loss of cartilage, you may be a very small amount shorter overall. With one hip involved, you will have one leg shorter than the other but overall height won't be affected much.