A numerical model for atmospheric aerosol nucleation bursts is presented as a tool for the analysis of measurements. It includes a minimum of physical assumptions and 94 user-controlled parameters. The model is based on computationally efficient parametrization of submodels, which allow considering the ion-induced and homogeneous nucleation, depletion of nanoparticles and ions on the pre-existing aerosol, the nano-Kohler growth function, the molecule-particle interception geometry, quantum retardation of sticking, the electric charges of particles, the molecular dipole moments, and the polarization interaction. The evolution of the size distribution is computed using a sectional model with several thousands of sections. Computing time on an ordinary PC is counted in seconds in case of a typical task with several thousands of time steps and several thousands of size sections. (C) 2004 Elsevier Ltd. All rights reserved.