The evolution of self-assembled InAs quantum dots grown by molecular beam epitaxy on GaAs(0 0 1) substrates was investigated as a function of the amount of InAs deposited on the surface. A single highly inhomogeneous sample was intentionally grown, where the thickness of the InAs layer varied in such a way that the InAs islands could be continuously analyzed from nucleation to coalescence, avoiding problems of reproducibility and thickness control that are common when a discrete set of samples is used. Extremely careful atomic-force microscopy measurements were carried out at many different locations of the sample and showed for the first time, unambiguously, that the size (height and diameter) histograms of the quantum dots become narrower and tend to an equilibrium value when the amount of InAs increases. (C) 2002 Elsevier Science B.V. All rights reserved.