While I can't tell for sure the mounting principles used from the images you provide, my Wolf island hood is bolted to its extension and that is lag screwed into the joists above the ceiling. The duct lives within the extension.

For your first image, I imagine that there is an internal duct, and either the extension pieces are bolted together with the hood bolted to the bottom extension, or alternatively, the entire stack could be pulled up by threaded rod or equivalent attached to the hood top and located in the corners between the circular duct and square extension column. Note that this requires a four-, not three-, sided extension, and the tile should extend completely across the wall between the cabinets. Small screws into the tile or grout could hold the assembly steady, perhaps only needed at the hood itself.

Complete tiling avoids several issues, and allows hood replacement approaches.

The circular extension of the second image is certainly supported from above and the tile of necessity has to be complete. Again, keeping the hood from "wandering" would require a couple of locating screws.

My question is more how does the duct deal with the transition between the tile and the wall? If you put the duct flat over the tile, then that would leave a gap between the duct and the wall where the tile stops.

You either use an island hood, or you install the hood and then install the tile around it.

Thanks. We don't want to tile around it ideally. How would an island hood duct work for this problem?

A wall hood + duct has only 3 sides (essentially). An island hood and duct has all 4 sides. And the gap remains if you don't tile to the ceiling. If you do tile to the ceiling, then a wall hood will leave no gap if mounted up to the tile. Note that the chimney most likely hangs from the ceiling and is not mounted to the wall (as opposed to the wall hood itself).

GreenDesign's comment, supplemented by weedmeister's comment is the most succinct. I was imagining using a four-sided duct cover and tiling the entire space including behind it. Then no grout to cover interface is needed. Note that the tile grout will not bond well to the stainless steel, and with different thermal coefficients of expansion, will crack there anyway. Some grout colored silicone would be needed.

One could tile to the ceiling or not. Unless the duct cover is kept away from the wall, island hood style, a close fit will avoid having to clean behind it. If the tile stops before the ceiling or soffit, then there will be a gap on the wall side that will be difficult to clean without an air gun. To avoid that the three-sided solution with tile installation last can be used.

So even an island hood wouldn't eliminate the gap between the hood and wall if I don't tile to the ceiling?

Island hoods are normally symmetrical, front-to-back, and have centered duct configurations. For any practical island hood front-to-back depth, the duct cover depth will be much less than that of the hood and hence there will be a large enough gap between duct cover and wall to clean behind it.

Careful examination of your first link shows an island hood with a gap to the wall behind it. The second link also appears to show an island hood. Neither of these hoods is particularly optimal from a performance point of view, but do bring the duct away from the wall allowing complete horizontal tiling and allowing a tiling edge at the cabinet tops.

The alternate idea under discussion was a wall hood using a four-sided island hood duct cover vs. a regular wall hood three-sided duct cover.

I think you're right - the first link is an island hood (I'm unable to edit the original post). The second link is a wall hood though, the Zephyr Anzio, which is the same one I'll be installing.

How would a wall hood with a 4 sided island duct solve the gap between the wall and the duct, above the tile line? I don't want there to be a gap at all.

If you don’t want a gap, the tile is installed after the hood. There is nothing wrong with that installation. Professional tilers do that all day long.

What is the tile you are installing?? If it is something intricate, then tile behind the hood and pad out behind the upper stack , caulk and paint.

Normally we do exactly what Cook said - just tile around it.

Best of luck - post pictures for others to see...

All the responses are much appreciated.

The tile we're installing is Island Stone Palms. I'd say it's somewhat intricate, and the color we're installing would leave noticeable gaps if we had to fill too many gaps to fill if tiling around the hood. That said, we'll definitely think about it.

http://www.islandstone.com/product/palms/

That tile is beautiful - I would run it to the ceiling!

We decided not to run the cabinets to the ceiling since it's a small kitchen and didn't want them to feel that heavy. Having the tile to the ceiling when the cabinets are not looks a bit off IMO.

Just stop the tile right underneath the hood rather than carry it up behind the chimney.