The primary purpose of the study is to provide expanded access of T-cell depleted haplo-identical stem cells for patients receiving allogeneic transplantation from a related haplo-identical donor and an unrelated, umbilical cord blood (UUCB) unit(s) for the treatment of high risk malignancies and non-malignant disorders. The T-cell depleted haplo-identical stems cells are intended to facilitate early, short-term myeloid engraftment with the primary goal of minimizing early infections and other non-relapse mortality while the UUCB cells engraft as the durable and permanent graft. Patients with high risk or refractory malignancies, or non-malignant disorders amenable to stem cell transplantation therapy but lacking conventional related or unrelated donors will be eligible for this protocol.