A paper-making machine and process, in which a paper web passes over a pope roller to a main roll and a new roll can be brought into contact with the pope roller when the main roll becomes a full roll, is improved by arranging at least two paper cutting tools to cut a paper web from each of two outer lateral edges to form two or more leader portions. A tail of the paper web formed on the full roll is symmetric and the leader portions on the new roll are also symmetric. Adhesive spray or tape can be applied to the paper web in the area of the leader portions. Air jets can also be used to bias the leader portions towards a surface of the new roll.