I've got a set of IKEA bookcases. Each one is roughly 30H x 30W x 14D
and is divided into 4 square sections. There are 4 and a half of them,
the "half' being half as wide, with only two sections.

They are lined up against a wall in our family room and come within a
couple of inches of taking up the whole wall, about 13'.

They are probably ten years old, and are thus somewhat better than the
current crop of IKEA stuff. It's their "Beech" finish. But for the
tops, which have gotten a little scratched up, they don't look too
bad.

I'd like to make a top that spans the whole set. I'm thinking of using
ceramic or porcelain tile with a wood 1x2 border around it. My
original idea would be reasonably easy, I think. 3/4 ply with the 1x2
glued around the edge to make a "tray" that the tiles would sit in.
Maybe I'd get fancy and rout out a dado in the 1x2 (oak, probably) for
the edge of the ply to fit into.

I might not even bother to use thinset or grout, perhaps just laying
the tiles in, or maybe using some construction adhesive. I have a tile
saw, BTW. I would use large tiles that span the entire depth with one
tile.

I think I'd have to build it in situ. There would have to be two
lengths of ply to cover the distance, and other than the "border" and
the furniture underneath, I don't know how I could fasten them
together well.

But then I had another idea, a wrinkle that I can't get in my head how
to accomplish. I have a bunch of prefinished IKEA kitchen molding,
3/4" thick, maybe 3" wide, straight except for a 1/4 round on one
side. It matches the cabinets well. I was thinking of using that,
laying flat, as the border. The benefit is that I wouldn't have to try
(and fail) to match the finish.

The problem is how to attach molding that thin to some sort of base
for the tiles. I'm thinking I could make a rabbet on the underside of
the molding to accept 1/4" or maybe 3/8" ply and then glue it up.
There'd almost certainly be a lip; the tiles wouldn't be exactly flush
with the surface of the molding. This might still look OK though.

Any thoughts? I'm not a complete idiot around wood and tools, but my
skills are modest, so be gentle.