Inclusion Criteria:

• Age 4 - 50 years
• Patient should not have a related or unrelated volunteer donor that is suitably HLA matched and available in the required time period or be a suitable candidate for an autologous stem cell transplant.

• Patients will have one of the following hematological malignancies: Acute myelogenous leukemia (AML):

  • Complete first remission (CR1) at high risk for relapse as defined by:

known prior diagnosis of myelodysplasia (MDS); or therapy related AML; or White cell count at presentation > 100,000; or Presence of extramedullary leukemia at diagnosis; or Unfavorable FAB type (M0, M5-7); or High-risk cytogenetics (those associated with MDS, abnormalities of 5, 7, 8, Philadelphia chromosome, complex karyotype); or Requirement for 2 or more inductions to achieve CR1

• Complete second CR (CR2).

  • Acute lymphoblastic leukemia (ALL):

• Complete first remission (CR1) at high risk for relapse as defined by:

White cell count at presentation as follows:

• > 100,000 if < 18 years
• > 50,000 if > 18 years; or

Presence of extensive extra-medullary disease (excluding CNS disease); or Presence of high-risk cytogenetic abnormality such as t(9;22), t(1;19), t(4;11) or other MLL rearrangements (11q23), t(8;14) [excluding B-ALL in pediatric patients]; or

Failed to achieve complete remission after four weeks of induction therapy

• Complete second or third remission (CR2 or CR3)

  • Acute undifferentiated leukemia (AUL), infant leukemia, or biphenotypic leukemia in CR1, CR2 or CR3. Patients with infant leukemia must be eligible to receive total body irradiation.
  • Juvenile Myelomonocytic leukemia (JMML) with < 30% bone marrow blasts.
  • Chronic myelogenous leukemia (CML)
• GleevecTM failure in 1st or 2nd chronic phase;

• Gleevec failure in 1st or 2nd accelerated phase.

  • Myelodysplastic Syndrome (MDS) with one of the following:

• Low (Score 0) International Prognostic Scoring System (IPSS) score with Life-threatening cytopenia(s); or Red cell or platelet transfusion dependent
• Intermediate (Score 1) or High (Score 2) International Prognostic Scoring System (IPSS) score.

• Patients with bone marrow blasts > 10% should have AML induction therapy with disease response to < 5% blasts and at least partial count recovery.

  • Non-Hodgkin's Lymphoma

• Patients with high-grade disease in PR1 following initial therapy and are not appropriate for further chemotherapy or autologous stem cell transplantation.
• Patients with high-grade or diffuse large cell NHL with recurrent disease after first remission and must have:

Chemo-sensitivity as evidenced by > partial remission (PR) (defined as > 50% reduction in mass size after therapy).

• Patients with adequate organ function and performance status criteria as measured by:
• Karnofsky score > or = to 70 % or Lansky score > or = to 70%
• Renal: Calculated creatinine clearance > or = to 60 ml/min
• Hepatic: Total bilirubin < 2.5 mg/dL unless benign congenital hyperbilirubinemia (Gilbert's syndrome) and ALT/AST < 3 x upper limit of normal
• Albumin > or = to 2.5
• Pulmonary: Pulmonary function (spirometry and corrected DLCO) > or = to 60% normal if available (in small children use History and Physical and CT scan as necessary to determine pulmonary status)
• Cardiac: Left ventricular ejection fraction > or = to 50%
• Double Unit Umbilical Cord Blood Grafts:

Units will be selected based on the HLA match to the patient as well as to each other and on the basis of the individual and combined cell doses of the units.

• Patient has a related or unrelated volunteer donor that is suitably HLA matched and available in the required time period.
• Patient is a candidate for an autologous stem cell transplant.
• Active CNS leukemia.
• Acute Myelogenous Leukemia in greater than CR2.
• Acute Myelogenous Leukemia evolved from myelofibrosis.
• Acute Lymphoblastic Leukemia, acute undifferentiated leukemia, biphenotypic leukemia or infant leukemia greater than CR3.

• Any acute leukemia with:

  • Morphologic relapse or persistent disease in the BM (cytogenetic relapse without morphologic evidence of relapse or cytogenetic persistent disease in the BM is acceptable); or
  • Active extra-medullary leukemia; or
  • Requiring greater than 2 cycles of chemotherapy to obtain present remission status;
• Bone Marrow aplasia (defined as BM cellularity less than 5% at transplant work-up); or
• MDS with greater than 10% bone marrow blasts refractory to chemotherapy; or
• CML in blast crisis; or
• NHL refractory to chemotherapy (less than PR after 2 or more regimens); or
• Prior autologous or allogeneic HSC transplant at any time; or
• Prior radiation therapy rendering patient ineligible for TBI; or
• Uncontrolled viral, bacteria or fungal infection at time of study enrollment; or
• Seropositive or NAT positive for HIV; or
• Females who are pregnant or breast feeding; or
• Patient or guardian unable to give informed consent or unable to comply with the treatment protocol including appropriate supportive care, follow-up, and research tests.