We model shell formation of core-shell noble metal nanoparticles. A recently developed kinetic Monte Carlo approach is utilized to reproduce growth morphologies realized in recent experiments on core-shell nanoparticle synthesis, which reported smooth epitaxially grown shells. Specifically, we identify growth regimes that yield such smooth shells, but also those that lead to the formation of shells made of small clusters. The developed modeling approach allows us to qualitatively study the effects of temperature and supply the shell-metal atoms on the resulting shell morphology, when grown on a pre-synthesized nanocrystal core.