Stochastically assembled nanoscale architectures have the potential to achieve device densities 100 times greater than today's CMOS. A key challenge facing nanotechnologies is controlling parallel sets of nanowires, such as those in crossbars, using a moderate number of mesoscale wires. Three methods have been proposed to control NWs using a set of perpendicular mesoscale wires. The first is based on nanowire differentiation during manufacture, the second makes random connections between nanowires and mesoscale wires, and the third, a mask-based approach, interposes high-K dielectric regions between nanowires and mesoscale wires. All three addressing schemes involve a stochastic step in their implementation. In this paper we analyze the mask-based approach and show that a large number of mesoscale control wires is necessary for its realization.