Rechargeable battery chemistries, with high energy densities, are particularly desirable in order to meet the burgeoning demand for energy storage. In this regard, metal electrodes have recently drawn extensive research interest due to the intrinsic energy density boost, while a fundamental study is needed to reveal the underlying mechanisms governing the electrodeposition stability. Here, we explore the mesoscale interactions in nucleation and growth of electrodeposition, with a focus on the competition of ion transport in the electrolyte, electrochemical reactions at the electrolyte-electrode interface, and surface self-diffusion. It is found that lithium (Li) and sodium (Na) metal anodes have the tendency to form dendrites at high local reaction rates, whereas magnesium (Mg) and aluminum (Al) do not, because of the low intrinsic self-diffusion barriers. Nonuniform electrodeposition at low reaction rates is observed, which could be attributed to the spatial inhomogeneities due to separator wetting, solid electrolyte interphase (SEI) formation, and electrode surface roughness. This work provides a fundamental understanding of the mesoscale underpinnings on the electrodeposition stability of various metal electrodes, especially shedding light on pathways toward potentially dendrite-free electrodeposition morphology.