Dense ocean water is formed primarily at high latitudes, but also in certain marginal seas in warmer areas. The main pathways of this dense water as it moves along the continental slopes is the topic addressed here. An analytical model describing how a geostrophic flow, with the aid of bottom friction, may lean on topographic irregularities and descend downhill toward the deep sea is presented. It is suggested that along-slope variation of the topography is a key element controlling the downward transport of dense bottom water. Deep corrugations can channel more water than shallow, but the transport also depends on their width. On gently sloping topography a maximum downward flow is induced by rather wide canyons (tens of km across), but in steeper regions the most active canyons are only a few km wide.The theory is applied to the continental slope east of Greenland, and it is shown that the transport capacity of this slope is sufficient to redistribute the Denmark Strait Outflow water from the level of 400m (at the Strait) down to below 2000m (at the southern tip of Greenland), which is consistent with observations. Application of the theory to the Faroe-Bank Channel (downstream of the sill) is consistent with observations from that region.