Toilet Paper holder - Extended

This is designed for when your toilet paper holder doesn't have enough room for the larger toilet paper rolls. In our place the TP drags against the wall when we pull out the paper. This will friction fit over the ends of the already existing spindle that came with ours.
I don't know if there are proper names for the parts of the toilet paper holder, but these are the names that I'm going with. The tube that goes through the toilet paper, I'm calling the spindle. The part that sinks into