This is a phase II study to assess the day 180 event free and overall survival after administration of a specified combination of fludarabine, busulfan, Total Body Irradiation (TBI), and thymoglobulin reduced intensity conditioning and 2 unit UCB stem cell transplant in a single institution setting in patients with hematologic malignancies for whom allogeneic transplantation is indicated.

Inclusion Criteria:

Subjects 18-70 years old. ECOG 0-2

Patients must have a diagnosis of one of the following:

• Chronic Myeloid Leukemia
• Acute Myeloid Leukemia
• Acute Lymphoblastic Leukemia
• Hodgkin's Disease
• Non-Hodgkins Lymphoma
• Myelodysplastic Syndromes
• Myeloproliferative Disorder

Patients must have adequate visceral organ function

• Patients must furnish written informed consent and HIPAA authorization for release of personal health information.
• Patients must be able to understand the requirements of the study, abide by the study restrictions, and agree to return for the required assessments.

Exclusion Criteria:

• Patients who have a histocompatible sibling-matched donor age 18 to 65 years in good health who is willing to donate stem cells are ineligible.
• Patients who are pregnant are ineligible.
• Patients are ineligible if they have received cumulative chemotherapy doses in excess of: carmustine (BCNU) 400 mg/m2, and/or a cumulative anthracycline exposure in excess of 550 mg/m2 doxorubicin (Adriamycin®) unless gated-pool radionuclide cardiac scan shows greater than/equal to 45% ejection fraction.

Patients who are HIV or HTLV-I, -II antibody sero-positive are ineligible.