The inhalation of micron-sized aerosols into the lung's acinar region may be recognized as a possible health risk or a therapeutic tool. In an effort to develop a deeper understanding of the mechanisms responsible for acinar deposition, we have numerically simulated the transport of nondiffusing fine inhaled particles (1 mum and 3 microm in diameter) in two acinar models of varying complexity: (i) a simple alveolated duct and (ii) a space-filling asymmetrical acinar branching tree following the description of lung structure by Fung (1988, "A Model of the Lung Structure and Its Validation," J. Appl. Physiol., 64, pp. 2132-2141). Detailed particle trajectories and deposition efficiencies, as well as acinar flow structures, were investigated under different orientations of gravity, for tidal breathing motion in an average human adult. Trajectories and deposition efficiencies inside the alveolated duct are strongly related to gravity orientation. While the motion of larger particles (3 microm) is relatively insensitive to convective flows compared with the role of gravitational sedimentation, finer 1 microm aerosols may exhibit, in contrast, complex kinematics influenced by the coupling between (i) flow reversal due to oscillatory breathing, (ii) local alveolar flow structure, and (iii) streamline crossing due to gravity. These combined mechanisms may lead to twisting and undulating trajectories in the alveolus over multiple breathing cycles. The extension of our study to a space-filling acinar tree was well suited to investigate the influence of bulk kinematic interaction on aerosol transport between ductal and alveolar flows. We found the existence of intricate trajectories of fine 1 microm aerosols spanning over the entire acinar airway network, which cannot be captured by simple alveolar models. In contrast, heavier 3 microm aerosols yield trajectories characteristic of gravitational sedimentation, analogous to those observed in the simple alveolated duct. For both particle sizes, however, particle inhalation yields highly nonuniform deposition. While larger particles deposit within a single inhalation phase, finer 1 microm particles exhibit much longer residence times spanning multiple breathing cycles. With the ongoing development of more realistic models of the pulmonary acinus, we aim to capture some of the complex mechanisms leading to deposition of inhaled aerosols. Such models may lead to a better understanding toward the optimization of pulmonary drug delivery to target specific regions of the lung.