Over the past decade, umbilical cord blood transplantation has been shown to be a viable alternative donor stem cell source for hematopoietic cell transplantation in subjects with catastrophic diseases treatable with transplantation therapy. UCB cells can cross partially mismatched HLA barriers without intolerable acute or chronic Graft-versus-Host Disease(GVHD). Thus, many subjects lacking a sufficiently matched, living related or unrelated bone marrow or adult stem cell donor, can use partially HLA-matched UCB cells for stem cell rescue after myeloablative irradiation and/or chemotherapy. UCB Cell dose, expressed per kilogram of recipient body weight, is the best predictor of outcomes after UCB transplantation. Cell dose thresholds strongly correlating with outcomes have been identified.