We use a novel path-density transport diagnostic to trace out the deep branch of the ocean conveyor in a global circulation model. Our results suggest that the majority of the world's deep water is not transported back to the surface along the current systems of the standard great ocean conveyor (GOC). Standard GOC routes are evident only for waters with interior residence times, τ, less than about a thousand years, accounting for less than a quarter of the ventilation-to-re-exposure flux. Waters with longer τ are spread across the deep oceans by the "diffusive conveyor" and, by τ ~ 3000 years, organized into a characteristic deep-North-Pacific pattern that is dominated by eddy diffusion. The observed depletion of oxygen and 14C in the deep N Pacific is consistent with a diffusive conveyor and should not be interpreted as evidence of an advective terminus of the GOC deep branch.