This study is an open-label, controlled, multicenter, international, Phase III, randomized study of transplantation of NiCord® versus transplantation of one or two unmanipulated, unrelated cord blood units in patients with acute lymphoblastic leukemia or acute myeloid leukemia, myelodysplastic syndrome or chronic myeloid leukemia, all with required disease features rendering them eligible for allogeneic transplantation.