I want to fill the space between my tub and the tiled wall. The space is about 1/2 inch thick. What is the beat filling to use
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Around the edges of the tub, 1/2" horizontally, or outside, 1/2" vertically?

Tubs have a lip around 3 sides to keep water from getting down behind the wall. It's standard to tile down closer to the tub and run a bead of silicone caulk around the edge, standing in the tub while full of water.
If you mean the outside edge, just get some 1/2" tiles that match or contrast, if you want. Or paint with semi-gloss paint.

Any chance of a picture?

If it is 1/2" opening, you should try to grout it with matching sanded grout mixed with acrylic mix. Opening is just way too large for caulk. You could also purchase 1/4" round edge tile and install it on thin set around the tub and grout it with non-sanded grout.

However, I would first try to find out why is that gap there. Is the tub settling ? Is it sitting on rotten framing ? Investigate first and if any structural defect is found, repair it first - or the gap will re-appear no matter what you fill it with.

Back to you

Milo