I was in this apartment many years ago when it was gutted. The units, which are close to 60 years old, do not have externally vented range hoods. The original units, I believe, had nothing. More currently upgraded units have recirculating hoods.

I asked the owner if they were going to put in an island hood, because the owner did have access in this unit to an external duct from an old bathroom. The answer was, no, probably something more low profile, closer to the ceiling.

I had assumed a high mounted insert in a shallow box or something, but what we have here is a regular room exhaust fan.

I know this is a bad idea, and is not very effective.

But, it appears that it is actually capturing something, because look how dirty it is. I know the homeowner has a very restricted diet and they are not doing a lot of flaming saute or anything that would splatter all the way up to the ceiling because the stove is so fired up. The weak fan must be pulling something, which is not exactly "nothing at all" which would be the conventional wisdom about something like this.

I did block out a few personal items, but I did not alter anything on the ceiling.