This is a single arm phase 2 study to obtain a preliminary estimate of efficacy of myeloablative double unit umbilical cord blood transplantation (UCBT) as measured by overall and disease-free survival at 1 year post transplantation. The UCB graft will consist of two (or double) units from two unrelated newborn donors. Patients with hematopoietic malignancy at high-risk for relapse or with advanced disease will receive myeloablative conditioning with cyclophosphamide (Cy),low dose fludarabine (Flu) and total body irradiation (TBI) with post transplantation cyclosporine (CSA) and mycophenolate mofetil (MMF) for GVHD prophylaxis.