So any safecoin that splits would not exist as a safecoin, so say you used a cent (for want of a better name) then the safecoin the cent came from is gone, its now 100 cents (it can become a safecoin again though and this is where the implementation can be very interesting and requires a lot of consideration), so no further increase in capital etc. is required. This seems fair and reasonable to me and I would really hope that if it went completely mad, then we would see a flattening out of money across the globe. Right now the $ is worth next to nothing in USA but several meals in other parts of the world. It would be nice if it were just the same everywhere, but good ol government’s eh! they always make sure there is somebody to screw with.
Anyhow that goes into a huge discussion where folk can be called crazy 
for now I think the answer to your question is new coins do not appear, it’s old coins that split.