The effect of separator pore size on lithium dendrite growth is assessed through the use of the phase field method (PFM). Dendrites are found to undergo concurrent electrodeposition and electrodissolution that define their local growth or shrinkage. Moreover, dendrites are observed to detach due to localized electrodissolution and generate metallic debris that is detrimental to battery performance. A critical current density exists below which dendrites are fully suppressed. An analytical model based on the performed PFM simulations allows to formulate the critical current density as a function of separator morphology and pore radius. Four distinct regimes of dendrite growth are identified: (i) the suppression regime, where dendrite growth is thermodynamically unfavorable; (ii) the permeable regime, where dendrite growth is prohibited beyond the first layer of the separator; (iii) the penetration regime, in which dendrites are stable within the channels of the separator; and (iv) the short circuit regime, where dendrites penetrate the entire width of the separator causing a short circuit. The identification of these regimes serve as a guideline to design improved separators.