Solid Hardwood, Engineered and Laminate Flooring - Hardwood and Tile with no transitions

I have carpet and tile right now with no visible transition between the two. Where the carpet ends, the tile starts very nicely at the same height. I want to do this with my hardwood installation. I don't like those T-joints that are raised above the height of the hardwood & tile.

How do I do this? instinctively, I was thinking of just running the wood right up to the tile but I've been hearing so much about a 1/4" gap to allow for expansion.

Please advise.

Use an engineered wood, and you may get by with a very small gap, to fill.

All wood needs an expansion gap, regardless of what you want.

If you use engineered wood, you can make that transition fairly easily as mentioned above. If you use 3/4 true hardwood, the level of the wood floor will, more than likely, be above the level of the tile, requiring some sort of transition.

My flooring is engineered 3/8" thick and my underlay is going to be .14". This will add up to 0.515". I'm hoping (and will find out as soon as I pull up the carpet) that this will be about the height of my current slate tile flooring (with underlay).

So if I have a "small gap to fill", what do I fill it with?

See my drawing below (T stands for Tile and H for Hardwood).

TTTTT <GAP> HHHHHH

I don't want the <GAP> to have anything that is higher than the Tile or the Hardwood. So when walking over it and stepping on it, I don't want to feel anything. Can I fill it with a caulking or something to allow expansion or do I just leave the GAP empty?

You can buy a matching wood filling caulk that will fill the void well - and allows for expansion of the wood down the road to some extent.