An apparatus and a production process for producing rolls of disposable pieces of hygienic paper, including the stages of: cutting perforated lateral lines on said hygienic paper, wherein each of the lateral spaces of the perforated lateral lines is shorter than each of the lateral perforations of the perforated lateral lines, wherein each of said lateral spaces is facing one of the lateral perforations of a neighboring perforated lateral line, rolling the hygienic paper around inner tube, and cutting longitudinal cuts along the hygienic paper and the inner tube, the apparatus including spiral and segmented blades for cutting the perforated lateral lines, and knives for longitudinal cutting.