Bipolar resistive switching memories based on metal oxides offer a great potential in terms of simple process integration, memory performance, and scalability. In view of ultrahigh density memory applications, a reduced device size is not the only requirement, as the distance between different devices is a key parameter. By exploiting a bottom-up fabrication approach based on block copolymer self-assembling, we obtained the parallel production of bilayer Pt/Ti top electrodes arranged in periodic arrays over the HfO2/TiN surface, building memory devices with a diameter of 28 nm and a density of 5 × 1010 devices/cm2. For an electrical characterization, the sharp conducting tip of an atomic force microscope was adopted for a selective addressing of the nanodevices. The presence of devices showing high conductance in the initial state was directly connected with scattered leakage current paths in the bare oxide film, while with bipolar voltage operations we obtained reversible set/reset transitions irrespective of the conductance variability in the initial state. Finally, we disclosed a scalability limit for ultrahigh density memory arrays based on continuous HfO2 thin films, in which a cross-talk between distinct nanodevices can occur during both set and reset transitions.