Cooper minima are known to profoundly affect photoionisation cross sections. They become particularly important in high-Z atoms where relativistic effects split each nonrelativistic Cooper minimum into three minima (two for s states). In addition, there are significant splittings in these 'triplets'. In this paper, the systematics of these relativistic Cooper minima are explored, over a broad range of elements, for 5p, 5d, 6s and 6p subshells. The phenomenology is presented and the physics behind the results discussed. In addition, the important implications for branching rates and photoelectron angular distributions are presented.