Busulfan and Cyclophosphamide Instead of Total Boby Irradiation (TBI) and Cyclophosphamide for Hematological Malignancies Hematocrit (HCT)

Inclusion Criteria: * Suitable cord blood from matched unrelated or related donor. * Cardiac (Echo/EKG): shortening fraction ≥ 27% * Electrolytes within normal CCHMC limits. * Pulmonary function tests: DLCO ≥ 50% * Renal: creatinine clearance/GFR ≥ 60 ml/minute/1.73m2 * Lumbar puncture: no leukemic infiltrate. * CBC: ANC ≥ 1000ml and unsupported platelet count of ≥ 50,000/ml * Documented HSV and CMV titers, Hepatitis B surface antigen, Hepatitis C by serology, HIV by serology: all negative. * Hepatic transaminases \< 2.5x normal; Total bilirubin \< 2 mg/dl Patients who do not meet above organ function criteria (liver, cardiac, renal), due to the presence of a tumor compromising these organs, may have exception made for these criteria and remain eligible for treatment plan after consultation with Program Director of Blood and Marrow Transplant Exclusion Criteria: * Patients with neoplastic or non-neoplastic disease of any major organ system that would compromise their ability to withstand the pre-transplant conditioning regimen. * Patients with uncontrolled (culture or biopsy positive) infections requiring intravenous antivirals, antibiotics, or antifungals. Patients on prolonged antifungal therapy with a history of fungal infection should be considered for a non-myeloablative protocol. * Patients who are pregnant or lactating. Patients of childbearing potential must practice an effective method of birth control while participating on this treatment plan. * HIV seropositive patients