Abstract. The origin of intraplate volcanism is not explained by plate tectonic theory, and several models have been put forward for explanation. One of these models involves edge-driven convection (EDC), in which cold and thick continental lithosphere is juxtaposed with warm and thin oceanic lithosphere to trigger convective instability. To test whether EDC can produce long-lived high-volume magmatism, we run numerical models of EDC for a wide range of mantle properties and edge (i.e., the oceanic–continental transition) geometries. We find that the most important parameters that govern EDC are the rheological parameters mantle viscosity η0 and activation energy Ea. However, even the maximum melting volumes predicted by our most extreme cases are insufficient to account for island-building volcanism on old seafloor, such as at the Canary Islands and Cabo Verde. Also, beneath old seafloor, localized EDC-related melting commonly transitions into widespread melting due to small-scale sublithospheric convection, inconsistent with the distribution of volcanism at these volcano chains. In turn, EDC is a good candidate to sustain the formation of small seamounts on young seafloor, as it is a highly transient phenomenon that occurs in all our models soon after initiation. In a companion paper, we investigate the implications of interaction of EDC with mantle plume activity (Manjón-Cabeza Córdoba and Ballmer, 2021).