PARITY $\notin$ $AC^0$ with bounded fanout: easy proof?
I might miss something, but isn't $AC^0_{bf}$ the same as a Formula? Since every input bit can have an effect on at most a bounded number of gates, we can simply suppose that every gate has only one output (after possibly duplicating a few things) and we can push down not gates as well. We know that the formula size of parity is n^2 (see Troy J. Lee, "The formula size of PARITY", 2007) and since on every level of our circuit we can only have O(n) gates, this shows that parity is not in $AC^0_{bf}$.