I would assume it depends on what registries. I don't really know on meat goats, although I think they can be registered on apperance like dairy goats (that would make them recorded grades, and their kids (only doe kids I think) would be %50, and get closer w/ each generation (assuming your breeding to registered bucks), w/ dairy goats eventually you will have kids that can be registered american. (atleast this is what I understand, I have a few full sized dairy goats, but mostly nigerian dwarfs which have different rules).
With nigerians (and I think pygmies) both parents have to be registered. There are three registeries for Nigi's ADGA, NDGA, and AGS. Some registries will accept goats already registered in a different association, making them double or even triple registered, I think both NDGA and ADGA will accept goats registered w/ AGS, but I don't think AGS will take goats registered only NDGA (not sure on ADGA). I have goats that are single, double, and triple registered, I get lazy sometimes, but I make sure everyone is atleast AGS registered.
Now there are also the mini dairy breeds (mini nubian, mini alpine, etc.) and I have no clue about their registries.