Soft, absorbent paper webs and processes for making them. In the process, an aqueous dispersion of the papermaking fibers is formed into an embryonic web on a first foraminous member such as a Fourdinier wire. This embryonic web is associated with a second foraminous member known as a deflection member. The surface of the deflection member with which the embryonic web is associated has a macroscopic monoplanar, continuous, patterned network surface which defines within the deflection member a plurality of discrete, isolated deflection conduits. The papermaking fibers in the web are deflected into the deflection conduits and water is removed through the deflection conduits to form an intermediate web. Deflection begins no later than the time water removal through the deflection member begins. The intermediate web is dried and foreshortened as by creping. The paper web has a distinct continuous network region and a plurality of domes dispersed throughout the whole of the network region.