The Pieces:
The system consists of basically feet, poles, shelves, and caps. There are 3 pole sizes, large, medium, and small. The poles have a male threaded rod at the top and a female threaded insert at the bottom. This allows the poles to be combined in many combinations to make different lengths—bigger than your print size—and to screw the feet on the bottom and the caps on top. You can add any number of shelves.
The poles come in three sizes: small, medium, and large.
Technical
To withstand and hold up better against the hot shower water, I printed the first prototype in ABS and this final version in PETG. Both work fine.
When printing the poles, I used a large brim of 10mm to 15mm. This is especially important when printing the taller poles. I have many a ruined pole because they came loose and were knocked over before they were finished printing :-(
It's really cool to be able to print one of these for yourself, but I reckon that it's just as easy to find something like this out there in the shops. Heck, you might be able to find similar pieces in the dollar shop if you hit the right outlets mate.