Waste paper is the answer to a composter’s prayer. just enough water

Soil animals and microorganisms need water. The bacteria and other microbes live in the film of water that covers compost particles, and most soil animals especially worms, the most important ones—are very intolerant of drying out. So obviously the ideal compost pile needs to be at least moist. But not too moist—too much water conflicts with the need for air, and there is no faster route to a smelly, anaerobic compost pile than waterlogging. The ideal water content for rapid composting is about 50–60 percent by weight, but knowing that isn’t very helpful, is it? In practice, this is the water content of a well-wrung sponge. How does this prescription square with the water content of typical compost materials? “Not very well” is the answer.

Kitchen waste and grass cuttings are at least 80 percent water, so a pile made entirely from such materials would be too wet, which would contribute to a lack of oxygen. You could solve the problem by adding drier, woody waste, shredded or otherwise, but this would slow things down too much. The solution once more is paper and cardboard, which not only lowers the average water content of the pile, but also soaks up the liquid that is released as the softer materials start to decompose.