A process for making an absorbent structure having a capillary substrate and regions of osmotic absorbent on the capillary substrate. The osmotic absorbent is cured from a liquid precursor applied to the capillary substrate. The capillary substrate has regions of topographically different elevations, taken normal to the plane of the capillary substrate. The capillary substrate is passed through a gap between a transfer roll and an anvil roll in a printing apparatus. The transfer roll has at liquid precursor on its periphery. The liquid precursor is applied to only the topographically elevated regions of the capillary substrate which contact the periphery of the transfer roll. By changing the topography of the capillary substrate, the liquid precursor can be applied to the capillary substrate in different pattern, without changing the transfer roll. This arrangement allows for absorbent structures having various patterns of osmotic absorbent on a capillary substrate to be readily produced with great flexibility in the manufacturing process.