Abstract We propose a simple method for calculating the on‐ and off‐axis neutral and negatively charged donors in axially symmetrical quantum dots whose thickness is much smaller than the base diameter. The adiabatic approximation is used to separate the slow in‐plane motion from the rapid transversal displacements. We show that the low‐lying free electron levels can be found by solving a two‐dimensional central force problem with effective potential whose shape strongly depends on the quantum dot profile in radial direction. The energies of the off‐axis neutral and negatively charged donors are calculated by using fractal dimension method. Novel curves and contour plots for the energies of donors confined in quantum disks, lens, pyramids and rings as functions of the base radius and the distance from the axis are presented. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)