When an aerocolloidal suspension flows through a fibrous filter, particles deposit on the fibers and form dendrites. Similar phenomena are observed with collectors other than fibers, provided that the characteristic dimension of the collector does not exceed that of the particles by more than one to two orders of magnitude. This deposition pattern leads to marked increases in capture efficiency and pressure drop, as particles accumulate within the filter. In previous publications, theoretical models of this process were developed for the cases of deposition by interception alone and of deposition by combined inertial impaction and interception. Consequently, those works apply to aerosol particles with diameters of 1 μm or larger. Here we extend the model to the case of submicron particles, where the main transport mechanism is Brownian diffusion. To keep things specific, we consider fine fibers as collectors, but the model can be easily converted to other geometries. We present solutions for the cases of nonslip flow around the fiber and nonslip, slip and free molecular flow around particles. Unlike deposition by inertial impaction and/or interception, convective Brownian diffusion forms dendrites over the entire fiber surface.