Local buoyancy forces drive the flow of ponded plume material along the base of the lithosphere. This processes complicates the geological effects of plumes beyond those of simple passage of plates over point heat sources. Variations in the depth to the base of the lithosphere significantly affect lateral flow. The flow rate is modified to a moderate extent by locally thin lithosphere beneath midplate hotspots, such as Hawaii. The effect is relevant when numerical models are rescaled to better fit the observed uplift and the observed distance from the hotspot to the nose of the swell. Variations in the depth to the base of the lithosphere have a much stronger effect on flow near ridge axes, effectively forming an upside-down drainage pattern. Plume material flows upslope toward ridge axes from off-axis plumes and along ridge axes from on-axis plumes at sufficiently low spreading rates. Thinner lithosphere exists above plume material than above normal asthenosphere. The edges of normal lithosphere adjacent to plume material act to some extent as levees which limit the lateral spreading of plume material. Pressure release melt is associated with the upslope flow of plume material. It is expected to cause volcanism away from the plume and to sometimes supply melt-depleted plume material to ridge axes that are upslope from the region of voluminous melting.