We report recent results on the homogeneous nucleation of GaAs quantum dots from organometallic precursors and subsequent heterogeneous nucleation of epitaxial regrowth of GaAs on the clusters. We find that clusters onto which we have regrown GaAs exhibit a much higher degree of faceting, whereas particles subject to che same thermal cycles but onto which no new GaAs has been grown, though crystalline, have highly irregular shapes. These results suggest that epitaxial regrowth exhibits selectivity in the growth rates on the various crystal facets akin to that found in bulk samples.