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We conjecture a new class of asymptotically locally AdS spacetimes, dual to a deconfined phase of a strongly-coupled field theory on a black hole background. We call these proposed spacetimes black funnels and black droplets, depending of the shape of the bulk black hole horizon. We examine the evidence for the existence of such solutions in lower-dimensional setting, focussing on realizations of funnels and droplets within the AdS C-metric family of solutions.