This paper presents a 3D Monte-Carlo model that simulates diffusion charging of aerosol particles in positive unipolar environments. Calculations are performed for N(i)t products up to 5 x 10(12) ions m(-3) s (with N-i being the ion concentration and t the charging time), and particles with diameter 5-1000 nm, covering a wide range of Knudsen numbers at atmospheric pressure. Apart from the average charge, the code allows for the calculation of the charge distribution which is shown to be well described by Gaussian statistics for monodisperse particles. Standard deviations of the charge distribution calculated with the source-and-sink approach show good agreement with the Monte-Carlo results. Comparison of the Monte-Carlo calculations with Fuchs' limiting-sphere theory shows good agreement for the whole size range and highlights the importance of the image force effect for smaller particles. The diffusion-mobility theory of the continuum regime matches the simulation results for the larger particle sizes while differences with Fuchs' limiting-sphere theory in this regime are relatively small. Simulations of non-spherical particles show the power of the code to easily handle more complicated situations. Results of rectangular-shaped and elongated chain-aggregate particles show different charging behaviour compared to theoretical predictions, and indicate the importance of the assumptions for the surface distribution of charges on the particle. In contrast, calculations of 3D cross-shaped aggregate particles, despite having a very irregular geometry, indicate that the spherical shape assumption is reasonable. (C) 2003 Elsevier Ltd. All rights reserved.