We demonstrate self-assembly of GaAs double quantum dots (DQDs) by droplet epitaxy in a lattice-matched system in addition to concentric quantum double rings (CQDRs). The growth mechanism of these complex nanostructures is understood by taking into account the two crystallization processes; the counter-migration (of Ga and As atoms)-induced crystallization and droplet-edge-enhanced crystallization. By tuning the balance between these two processes, completely different types of the coupled quantum nanostructures are created. (c) 2005 Elsevier B.V. All rights reserved.