A multi-ply absorbent sheet of cellulosic fiber with continuous outer surfaces is provided an absorbent core between the outer surfaces. The absorbent core includes a non-woven fiber network having: (i) a plurality of pileated fiber enriched regions of relatively high local basis weight interconnected by way of (ii) a plurality of lower local basis weight linking regions whose fiber orientation is biased along the direction between pileated regions interconnected thereby, and (iii) a plurality of fiber-deprived cellules between the fiber enriched and linking regions, also being characterized by a local basis weight lower than the fiber enriched regions. The cellules provide a sponge-like internal structure of low fiber density regions.