During the discharge of a lithium−sulfur (Li−S) battery, an electronically insulating 2D layer of Li2S is electrodeposited onto the current collector. Once the current collector is enveloped, the overpotential of the cell increases, and its discharge is arrested, often before reaching the full capacity of the active material. Guided by a new computational platform known as the Electrolyte Genome, we advance and apply benzo[ghi]peryleneimide (BPI) as a redox mediator for the reduction of dissolved polysulfides to Li2S. With BPI present, we show that it is now possible to electrodeposit Li2S as porous, 3D deposits onto carbon current collectors during cell discharge. As a result, sulfur utilization improved 220% due to a 6-fold increase in Li2S formation. To understand the growth mechanism, electrodeposition of Li2S was carried out under both galvanostatic and potentiostatic control. The observed kinetics under potentiostatic control were modeled using modified Avrami phase transformation kinetics, which showed that BPI slows the impingement of insulating Li2S islands on carbon. Conceptually, the pairing of conductive carbons with BPI can be viewed as a vascular approach to the design of current collectors for energy storage devices: here, conductive carbon “arteries” dominate long-range electron transport, while BPI “capillaries” mediate short-range transport and electron transfer between the storage materials and the carbon electrode