During metal-catalyzed growth of tapered silicon nanowires, or silicon nanocones (SiNCs), Au-Si eutectic particles are seen to undergo significant and reproducible reductions in their diameters. The reductions are accompanied by the transfer of eutectic droplet mass to adjacent, initially metal catalyst-free substrates, producing secondary nucleation and growth of SiNCs. Remarkably, the catalyst particle diameters on the SiNCs grown on the adjacent substrates are strongly correlated with those on the SiNCs grown on the initially Au-nanoparticle-coated substrate. These post-growth nanoparticle sizes depend on temperature and are found to be independent of the initial nanoparticle sizes. Our modeling and analysis indicates that the size reduction and mass transfer could be explained by electrostatic charge-induced dissociation of the droplet. The reduction in size enables the controlled growth of SiNCs with tip sharpnesses approaching the atomic scale, indicating that metal-catalyst nanoparticles can play an even more dynamic role than previously thought, and suggesting additional modes of control of shape, and of nucleation and growth location.