This blue roll dispenser uses gravity so that it is as close to the wall as it can be for the amount of roll left.

There is also an included cutter model, this utilises leverage to trap the blue roll against the wall stopping it from rotating allowing easy separation.

There are three different holders, screw mounting, Ikea Skadis mounting and one to mount onto Honeycomb storage wall by @RostaP allowing for many options for mounting this onto a wall.
There are also two style of rotation mechanisms, one utilises a 3D printed ‘snap bearing’ and another to use 15mm wooden dowel. This means that there are many options to keep it operating smoothly.

The two types of arms are designed to work with wooden dowel, 12mm and 8mm, one design has a static roll position where as on the other it is adjustable and could even hold multiple smaller rolls or tape.