What is "fine ground cornmeal"?
I'm an American cornbread lover living in the UK, so I have some experience with this. In the UK and commonwealth corn flour = US cornstarch, and in the UK corn meals are coarser then their US counterparts. Coarse polenta is like ball bearings, fine polenta is still too coarse for decent cornbread and fritters. You can get fine corn meal in the UK now, which is slightly finer than your average US cornmeal, but not as fine as US corn flour. 

So if I'm in the US using an American recipe that calls for fine corn meal I'd just use regular corn meal, if I'm in the US using a UK recipe and it calls for fine corn meal it would probably mean fine polenta, which is what you generally get in the US.