I worked on the design for a new tissue mill once, at Disley near Stockport, and then helped to commission it. The machine is about a hundred yards long and is made of stainless steel. The pulp is sprayed on to a continuous fine mesh belt abot 15 feet wide and the machine can make a roll of bog paper the same width and 10 feet in diameter in minutes! The rolls are then sent somewhere else for perforating and converting in to the rolls that we buy in the shops.
I think that the fibres align themselves as they are sprayed on to the belt, along the length of the roll, as indicated in previous posts.