I don't have my cases by year at hand, but by way of showing you how different things can be:
at my program Chief residents did not have independent operating privileges. We could not start a case, even an emergency one, without the attending being there. If we were lucky we could make an incision and start setting up the Bookwalter (if needed) before the attending scrubbed.
The attendings were present and scrubbed for almost the entire case. If we had a student on service, or a junior resident who happened to be scrubbed in, they would leave once the anastomosis was done and we would close with the student or intern. But often times they were there, skin to skin.
I thought it was just me, but my fellow Chiefs confirmed it was that way for them as well.