At fast and superfast spreading mid-ocean ridges, such as the East Pacific Rise, a plate boundary is defined by a narrow (tens to hundreds of meters wide) neovolcanic zone within which the bulk of the upper oceanic crust is created. However, detailed near-bottom observations indicate that the volcanic construction may occasionally persist several kilometers off of the ridge axis. It has been proposed that off-axis volcanism manifests tapping of a wide melting region that supplies magma to the ridge axis, or spatial migration of magmatic sources in the crust and upper mantle. We demonstrate that off-axis eruptions may be a natural consequence of variations in magma supply rate even if the ridge axis is stationary in space, and the magma delivery is perfectly focussed at the ridge axis. Theoretical modeling and field observations indicate that off-axis volcanism may result from magma emplacement in sills that propagate toward the surface after their characteristic horizontal size exceeds their emplacement depth. Volcanic construction and faulting due to sill intrusions may contribute to the formation of abyssal hills, arguably the most abundant relief form on Earth. ß