Planning to install on a diagonal in a 13.5' x 33' room. Below are pictures of the transition area to tile kitchen. Tile subfloor is 1/4" higher than hardwood subfloor for 3.25" exposed area. My plan is to use shingles and roofing paper to gradually raise the hardwood subfloor up to the tile subfloor level and then was planning to install two header rows parallel to the tile. Second header strip will be parallel to the subfloor joint and have ~ half its width on either side of the joint.

(1) The grout spacing on the tile is 3/16". How much space do I need to leave between the hardwood header and the tile to be filled with sanded caulk?

(2) The hardwoods will be between 3/32" and 7/64" higher than the tile (roofing paper will push it slightly higher). Would routing the edge of the first header strip closest to the tile coupled with the gap between this strip and the tile provide a smooth enough transition? Any other ideas?

(3) The transition area is 4.5' in width. The tile subfloor drops 7/64" over the last 18" on the right hand side. Do I need to be concerned with this drop? I am able to easily push 4' hardwood strip flush to the floor by pressing down on both ends.

http://flickcabin.com/public/viewset/4046

1) I like to try and match the same spacing as the tile has, unless the tile is butted tight. I use a 1/4" typically.

2) Consider tapering that board by standing it up on it's side and running it through a table saw set at 15 degrees. Then sand smooth and finish to match.

3) 7/64ths? Sorry, I don't deal in 64ths for flooring Seriously, it sounds too minor to worry about.

I like your idea of tapering the board as opposed to routing the edge. Thanks for the replies and confirmation that the drop off is too minor to worry about.