Normally the size dependence of the chemical potential is used to explain the growth dynamics of semiconductor nanoparticles. Instead we show that very small CdTe nanoparticles continue to grow at high dilution, the growth rate is virtually independent of monomer concentration, nucleation continues after the growth of larger particles has saturated, and the growth rate has a much greater nonlinear dependence on particle size than predicted by theory. We suggest that nanoparticle growth is fast in the liquid phase and then saturates as the particles change phase from liquid to crystal at a threshold size which depends on the growth temperature and not the monomer concentration. The photoluminescence quantum efficiency becomes high when tellurium is depleted in the reaction solution giving a cadmium enriched surface.