I have a small area in which I do a lot of crafts. My collection of wrapping paper seems to grow this time of the year. Here's a way I make my small area more efficient and a space saver with cup hooks, wood dowels and plastic or metal chains. I suspend the chains underneath my shelves and run my dowels through the chains. The chains are attached underneath the counter with cup hooks.
Once you use part of a roll of wrapping paper it is difficult to keep it from unwrapping from the tube. Try using another smaller diameter paper tube, cut up its length, to secure the cut edge. This is a page about using recycled cardboard tubes to hold wrapping paper.
Wrapping paper is notorious for unrolling. Finding a way to prevent this without wrinkling the paper too much can be a bit of a task. This is a page about keeping Christmas wrap rolls from unrolling.