You can get slim range hoods that generally fit into the wall cabinets ours were approx 40cm deep which housed the complete operation, our plumber ran a 6 or so inch flexable ducting into the roof cavity and out under the eaves. Most brands make these. A photo would be helpful. https://www.thegoodguys.com.au/omega-52cm-undermount-rangehood-oru50x?CAWELAID=620013790000422290&CAGPSPN=pla&CAAGID=21711678566&CATCI=pla-376401441757&gclid=CjwKCAjw0qLOBRBUEiwAMG5xMNN63iJr0n0Bnxf31-Gt0t5s0vERt_lOwOYkC6uzovf9TDWwawry9RoCgxQQAvD_BwE&gclsrc=aw.ds&dclid=CLOv9erawdYCFc0slgodE5oLHg Where we didn't have wall cabinets we had tall boxes of stainless look laminate built up to the ceiling which contained the extraction unit, which was approx 30-40cm's and extraction ducting cheers

there are several range hoods eg Miele that can be vented horizontally and even some that can vent downward under the floor and another that has the motor outside the walls but you'll need to check with manufacturers to clarify which one would suit as you need to know exactly where the wall and floor framing is located to make sure there's enough space for installation ..rear venting rangehoods don't use less cabinet space they just avoid having a pipe through the ceiling and roof...

Hello 61karwin, I do not have a range hood just an exhaust fan. I do not do much in the way of frying, I am however rather good at 'carbon' but find with a good breeze thru from open windows that it is no problem. The fan does need cleaning every now and then but I get a tall person to assist: a young one who is happy to get onto the bench! I do not see a problem unless your home is not well vented and you like cooking hot chips! Cheers Margot

For the small amount of range hood that would be in contact with the undulating subway tiles, I do not see a problem.