The ramified and stochastic evolution of dendritic microstructures has been a major issue on the safety and longevity of rechargeable batteries, particularly for the utilization of high-energy metallic electrodes. We analytically develop criteria for the pulse characteristics leading to the effective halting of the ramified electrodeposits grown during extensive timescales beyond inter-ionic collisions. Our framework is based on the competitive interplay between diffusion and electromigration and tracks the gradient of ionic concentration throughout the entire cycle of pulse-rest as a critical measure for heterogeneous evolution. In particular, the framework incorporates the Brownian motion of the ions and investigates the role of the geometry of the electrodeposition interface. Our experimental observations verify the analytical developments, where the dimension-free developments allows the application to the electrochemical systems of various scales.