A variety of geophysical and geochemical evidence indicates that ascending mantle plumes can interact with ocean ridges located up to 1400 km away. I investigate the dynamics of this interaction using a simple model in which a point source with volume flux Q (analogous to a plume ''stem'') releases buoyant fluid into a viscous corner flow driven by the divergence of rigid surface plates with thickness ~(&kgr;x/U)1/2, where U is the half spreading rate. The point source is located at a distance xp from the ridge, and ridge migration is neglected. The buoyant fluid forms a thin sublithospheric layer whose thickness S(x,y) satisfies a nonlinear advection-diffusion equation describing the balance of advection by the corner flow, buoyancy-driven ''self-spreading,'' flow toward the ridge along the sloping base of the lithosphere, and continuous accretion into the lithosphere. Numerical solutions of this equation yield scaling laws for the lateral extent W (''waist width'') of plume material along the ridge, the fraction R of the plume flux that crosses the ridge, and the maximum value of xp beyond which interaction ceases. The sloping base of the lithosphere has only a minor (few tens of percent) influence on these quantities, which are determined principally by the balance of advection and self-spreading. An extension of the model to include plume-induced lithospheric thinning shows that this process increases the waist width by an amount of order 10%. Finally, the model provides a new explanation for the observation that plumes interact primarily with ridges that are migrating away from them, rather than toward them. ¿ American Geophysical Union 1996