I leave it out overnight. I don't like to leave it on overnight, so what I do is I get it going early in the morning, let it cook for 12+ hours, then around 9 or 10 pm, turn the stove off, and take it off the burner. I let it cool overnight with the lid on, then in the morning, if I have time to strain it right then, I will, or else I just pop the pot in the spare fridge (which I won't have soon, when I move out
but I'll find a way to make it work) with the bones and stock and all, then in the next day or so when I have time, strain it and package it for storage (in jars, or flat in the freezer in plastic baggies.)
Last time I tried this, I think I didn't start it until noon and it didn't cook enough. It had very little flavor. After taking it out of the fridge to use and discovering this, I boiled it for oh 3 or 4 hours? It made a cloudy, jelly, delicious dark stock. (first jelled stock!!)