I know that the x and z coordinates of the Overworld have a relationship to the positioning of the associated portal in the Nether. How about the y coordinate? I know that the top of the Nether is only 127 so it cannot be a 1 to 8 relationship but is there any relationship? If I build a portal on the top of a mountain, does that mean in the Nether my portal would be higher? Same with depth. If I built it at level 1, wound I end up near Nether level 1?
The Nether has been 256 blocks high for quite a while, it's just that you need to find a way to get through the ceiling.
(It used to be that you couldn't use portals to get above the bedrock ceiling, now you can but portals above the ceiling may not auto generate so you probably have to get up some other way and build one.)
So the Y coordinates are 1:1
If you go through a new portal and the game can't find one close enough to the converted coordinates in the other dimension the game will try to build one as close as possible (except probably not in the top half of the Nether.)
In my experience, the game will try to match the Y coordinate, but it needs to be in open land of course, so it will adapt the location of the portal generated to make sure there is room to place it in all 3 dimensions. I've made portals at Y-30 in the overworld that end up 80 blocks high in the nether because there was land/trees below.
You can however move a portal in the Y dimension anywhere you like (assuming you remove the original) and it will connect to the same portal as the first did.
When trying to create a new portal, the game will look for valid locations within 16 blocks of target coordinate horizontally, but any distance vertically. However, if it finds multiple valid locations, it will pick the closest Euclidean 3D distance valid location available.
One generally should avoid building their first nether portal very deep, cause they easily might end up in a cave under lava ocean.