Roll-to-roll printing processes require formation and stretching of a liquid bridge to transfer liquid from one surface to another. Since inadequate liquid transfer can produce defects that are detrimental to printed products, electric fields are sometimes applied to enhance transfer, a method known as electrostatic assist (ESA). Because the physical mechanisms underlying ESA are not well-understood, we examine here the influence of electric fields on liquid transfer in two model geometries, both of which involve liquid bridges with moving contact lines. The bridges are axisymmetric and confined between two electrodes, one of which is flat and moves vertically upward, and the other which either is flat or has a cavity and is stationary. An electric field is applied in the axial direction, both perfect and leaky dielectric liquids are considered, and the governing equations are solved with the Galerkin finite-element method. For liquid transfer between two flat plates, application of an electric field stabilizes the liquid bridge. This allows more time for the contact line to retract on the less wettable surface and leads to an increase in liquid transfer to the more wettable surface. Tangential stresses due to surface charge can significantly enhance liquid transfer, even to the less wettable surface if the tangential stresses point toward that surface. For liquid transfer between a flat plate and a cavity, the electric field increases the pressure gradient near the contact line on the cavity wall, causing the contact line to slip and more liquid to be transferred from the cavity. Notably, the effect is more pronounced for a deep cavity, resulting in a larger percentage of liquid transferred compared to a shallow cavity. In contrast to the case of liquid transfer between two flat plates, surface charge does not have as significant an influence on liquid transfer due to the way the cavity and electric field modify the interface shape near the contact line. The results of this work illustrate the physical mechanisms through which electric fields can improve liquid transfer, and they provide guidance for optimizing ESA in industrial printing processes.