Physical properties of nanostructures are strongly influenced by their dimensions and shapes, so that only a precise control on the nanocrystals morphology can allow for the fine tuning of their electronic properties. The droplet epitaxy (DE) [1] is a flexible growth method, based on the molecular beam epitaxy, which allows for the fabrication of a large variety of three-dimensional nanostructures with different geometries. During the growth of GaAs by DE the substrate is first irradiated by a Ga molecular beam flux, leading to the formation of numerous, nanometer-size, Ga droplets on the surface with uniform size, which are subsequently crystallized into GaAs nanostructures by an As molecular beam supply. The intrinsic design flexibility of the DE variant of MBE is permitted mainly by such splitting in time of the III-column and V-column element supply. This allows an independent choice for each of the two elements of specific growth conditions. In this presentation a set of samples which showed a large morphological tunability, ranging from quantum dots (QDs) to quantum dots molecules (QDMs), quantum rings (QRs), concentric double quantum rings (CQDRs), concentric multiple quantum rings (CMQRs)[2], coupled rings/disks (CRDs) [3], Dot/Ring, Dot/Disk, Ring/Ring and Ring/Disk complexes, was successfully fabricated. The wide growth parameter space (defined by the substrate temperature and the As flux used for the crystallization) has been explored, studying the influence of the growth conditions on the nanocrystals configuration. We investigated the growth mechanism by means of Reflection High Energy Electron Diffraction (RHEED), Atomic Force Microscopy (AFM) and selective chemical etching. We introduce a model for the growth mechanism of GaAs nanostructures, which accounts for the fabrication of different types of nanostructure on the GaAs/AlGaAs system, based on the interplay between the As adsorption on the Ga-rich (4×6) surface and the Ga migration on the As-stabilized (2×4) activated by the substrate temperature and limited by the As impingement rate on the surface. [1] N. Koguchi, S. Takahashi, T. Chikyow, J. Crystal Growth 111 (1991) 688. [2] C. Somaschini, S. Bietti, N. Koguchi, and S. Sanguinetti, Nano Letters 9, 3419-24 (2009). [3] C. Somaschini, S. Bietti, S. Sanguinetti, N. Koguchi, and A. Fedorov, Nanotechnology 21, 125601 (2010).