When dilute solutions of nearly monodisperse (3-5-nm diameter) passivated metal nanoparticles are evaporated on a solid substrate (a transmission electron microscopy grid), the resulting submonolayer structures are annular ringlike arrays. We describe here a theoretical mechanism whereby the growth of holes-dry areas of the solid surface which is otherwise wet by solvent-is conjectured to be responsible for the formation of these novel close-packed two-dimensional (2D) arrays. Each annular ring is argued to arise from the pinning of the rim of an opening hole by a sufficient number of particles. Hole nucleation in this ultrathin-film system can occur due to two independent driving forces : evaporation (volatile hole nucleation) and disjoining pressure (nonvolatile hole nucleation). The cases are first presented separately, in an appropriate analytical theory, and are subsequently treated jointly in the context of a simulation. We investigate in particular the effect of competing time scales (for hole nucleation, fluid flow, and solvent evaporation) on the average diameter of the resulting ringlike configurations.