I could just toss my shredded paper into the trash but I like to reuse it here are some ways that I reuse it.
A weed barrier under mulch. The shredded paper is soaked for a day or so and then spread thickly where I will place mulch. It can be spread when dry but dry paper will blow away until mulch is being spread. The soak allows the paper to mesh together and form a better weed barrier. This does need to be replaced as often as regular cardboard weed barrier. It works as well as a weed barrier as cardboard, and is easier to plant through. As for moisture retention and soaking through, it seems to allow water to penetrate as well as cardboard and keeps water in as well as cardboard too. Obviously I do not use plastic barrier any longer. It took me ages to rip out the damaged barrier around my yard and I still find pieces of it. I think cardboard as a weed barrier is easier to install as it can be laid down dry, soaked with water from my hose and then have mulch placed on top.
I like cardboard as a weed barrier for so many reasons, but using the shredded paper seems to work as well, at least in the small areas where I have used it. I have noticed that it will shed water until the top layer is well soaked or if the shredded paper is domed to collect water. It seems to stay as wet as long as cardboard does.
I have detailed the art uses in another post, but this is an area I need to explore more.
I am considering the pulp may be used to create seedling pots- the pulp could be formed over a mold and then pressed to remove water, then removed. Much like the current peat pots available. Seems like a lot of work for something that would just be put into the ground though.
The toilet paper tubes- I make 4 slices on one end and then fold the ends to create a box bottom. These get loosely packed with soil and then seeds placed inside. The TP tubes do have a tendency to mold but work great even with mold. For plants that don’t like to be transferred, like beans, you can just stuff the tubes with soil without the box bottom and transplant them as is. I may attempt this method this year for everything. It is useful to have a container with higher sides to hold the TP tubes for this. I have in the past used recycled small cake covers, the clear sort that cover cakes at the grocery store. This allows watering from the bottom with ease.
Egg cartons- I save egg cartons for my mom but occasionally the saving of them starts to take up far too much space. I use these as paper pulp but also to create fire starters and for starting seeds. For seed starting I use egg cartons for salad greens and things like marigolds. I start seeds in them that start fast and won’t need to be in the egg carton for long. Egg cartons need a lot of support when wet but also dry very quickly. I have not noticed them molding but I also am only starting things that grow fast. egg cartons are my last and least favorite seed starting method- they are simply not deep enough for most seeds.
Egg cartons are great for pulp- there is a lot of paper pulp in a carton and are good for making molded things. They are good for paper mâché clay.
This is not an exhaustive list, please list the ways you might use pulp in the comments!