Nope, it hasn't been cut back at all.
This is what's known as a traditional 'London pattern' anvil, and that small flat just behind the horn is known as the 'table'.
Its purpose is to provide a soft, flat area for chisel cutting, so that the chisel [such as the 'hot chisel' head which is the second tool lying on top, from the horn end] doesn't put cut marks in the working face, or get blunted against hard metal. 'Hot chisel' because it's shaped for cutting metal which is 'hot', i.e. at red heat or above.
The first tool head is a 'top fuller' by the way, used for flattening out and spreading the hot workpiece. Like the chisel, this is a struck tool, used fitted to a light handle, and struck with a heavy hammer.
There's no maker's , or even weight, marks on this anvil. Haven't weighed it, but I'd say around the 50-70lb mark.
It's set at the traditional blacksmith's personal working height. That is, so that the knuckles of my closed hand will just rest on the face, with that arm held straight down.
