In this study, we take an alternative approach to facilitating early myeloid engraftment in subjects undergoing UCB transplantation therapy. In subjects who cannot only identify a donor delivering a cell dose >2 x 10^7 nucleated cells/kg, we will augment the UCBT with a lower dose of haplo-identical, T-cell depleted stem cells from a related adult donor to facilitate early, short-term engraftment with the primary goal of minimizing early infections and other non-relapse mortality while the UCB cells engraft as the durable and permanent graft. As the immunocompetent UCB cells engraft, we expect that they will reject the immunologically incompetent haplo-identical adult stem cells. Thus, after approximately 100-180 days post transplant, the subject should convert to 100% donor chimerism with the UCB donor graft.