Much of our understanding of the transport and deposition of inhaled fine (1 μm) and ultrafine (0.1 μm) aerosols in the deep regions of the lungs, where acinar airways are densely populated with pulmonary alveoli, revolves around the paradigm that inhaled aerosols are foremost affected by local acinar airflows. Until present, numerical efforts addressing such transport questions have largely discarded intrinsic Brownian motion compared to convective phenomena. Yet, it has been recently noted that for particles less than 1 μm acinar (ultra)fine aerosol transport is rather governed by the intricate coupling arising between convective and diffusive processes (Sznitman, J. Biomech., 2013). The increasing role of particle diffusion is further highlighted when considering the specific flow topologies within acinar airways, where local alveolar flows illustrate complex recirculating cavity flows that are orders of magnitude weaker relative to acinar ductal flow phenomena. In an effort to gain quantitative insight on the role of convective-diffusive mechanisms for acinar aerosol deposition, we present state- of-the-art numerical simulations under physiological cyclic breathing conditions for expanding and contracting septal wall domains using morphologically- inspired, multi-generation asymmetric alveolated tree networks. Here, we specifically investigate aerosol transport kinetics in the presence of stochastic Brownian motion, drag and sedimentation for particle diameters spanning more than two orders of magnitude. Overall, our efforts underline a new paradigm for predicting with fidelity the fate of inhaled fine and ultrafine aerosols in the deep ends of the lungs, under the combined mechanisms of particle convective- diffusive-gravitational transport.