We show that independent size and morphology engineering of epitaxial quantum dots can be obtained using a kinetically controlled quantum dot fabrication procedure, namely droplet epitaxy. Due to the far-from-equilibrium droplet epitaxy procedure, which is based on the crystallization, under As flux, of a nanometric droplet of Ga, independent and precise tuning of quantum dot size, aspect ratio, and faceting can be achieved. The dependence of the dot morphology on the growth conditions is interpreted and described quantitatively through a model that takes into account the crystallization kinetics of the Ga stored in the droplet under As flux.