We study the shape transformation of self-assembled InAs quantum dots on (001) GaAs during overgrowth with AlAs and subsequent thermal annealing. InAs dots are grown in Stranski-Krastanow growth mode at various growth temperatures, thickness of the AlAs cap layers, as well as post-growth annealing times and temperatures. Dependent on these parameters, we observe shape transitions of the initial InAs quantum dots e.g. into ring-like structures or a splitting into lateral double-dot molecules. (c) 2005 Elsevier B.V. All rights reserved.