Process for the production of paper rolls, including a step of producing logs (L) of paper material by winding a predetermined amount of paper web (W) about a tubular core (C) oriented transversely with respect to a direction (PP) of entering of the paper web (W) in a rewinder (R) in which the winding is executed, and a step of transverse cutting of the logs (L) to obtain rolls (R) of predetermined length. The cores (C) are produced by a tube-forming machine (T) whose position is intercepted by the direction (PP) of the paper (W) entering the Rewinder®.