DISEASE CHARACTERISTICS:

• Diagnosis of one of the following advanced hematologic malignancies:

  • Acute leukemia in remission by morphology (< 5% blasts) OR cytogenetic relapse or persistent disease without morphologic relapse*

    • Acute myeloid leukemia, meeting 1 of the following criteria:

      • High-risk disease as evidenced by 1 of the following criteria:

        • In first complete remission (CR) as evidenced by preceding myelodysplastic syndromes (MDS)
        • High-risk cytogenetics such as ones associated with MDS or complex karyotype
        • Required at least 2 courses to achieve CR
        • Erythroblastic and megakaryocytic
      • In second or greater CR

    • Acute lymphoblastic leukemia/lymphoma, meeting 1 of the following criteria:

      • High-risk disease in first CR, as evidenced by 1 of the following:

        • High-risk cytogenetics (e.g., t[9;22], t[1;19], t[4;11] or other mixed-lineage leukemia rearrangements)
        • More than 1 course to achieve CR
      • In second or greater CR NOTE: *Small percentage of blasts that is equivocal between marrow regeneration vs early relapse allowed provided there are no cytogenetic markers consistent with relapse

  • Chronic myelogenous leukemia

    • Patients with chronic phase disease must have failed or been intolerant to imatinib mesylate
    • No refractory blast crisis

  • Myelodysplastic syndromes (MDS)

    • Blasts must be < 5% (may achieve with induction therapy prior to transplant)
    • Any subtype including refractory anemia if severe pancytopenia or complex cytogenetics present

  • Large cell lymphoma*, Hodgkin's lymphoma*, or multiple myeloma, meeting 1 of the following criteria:

    • Chemotherapy-sensitive disease that has failed therapy
    • Patient ineligible for autologous transplantation

  • Lymphoplasmacytic lymphoma, mantle cell lymphoma*, or prolymphocytic leukemia

    • Must be chemotherapy sensitive after initial therapy NOTE: *No disease that has progressed on salvage therapy unless disease is stable and nonbulky.

  • Chronic lymphocytic leukemia/small lymphocytic lymphoma, marginal zone B-cell lymphoma, or follicular lymphoma, meeting 1 of the following criteria:

    • Disease progression after ≥ 2 prior therapies
    • Refractory disease allowed provided disease is nonbulky and an estimated tumor doubling time is ≥ 1 month
    • Patients with bulky disease (nodal areas > 5 cm) should undergo debulking chemotherapy before transplantation
  • Bone marrow failure syndromes (no Fanconi's anemia)

  • Burkitt Lymphoma

    • In CR2 or subsequent CR
  • Natural killer cell malignancy
  • Myeloproliferative syndromes

• Stable disease allowed provided the largest residual nodal mass is approximately < 5 cm

  • Largest residual mass must represent a 50% reduction and be approximately < 7.5 cm for patients who have responded to preceding therapy
• Disease not curable by conventional chemotherapy
• Patients with refractory leukemia or MDS may undergo transplant in aplasia after induction or re-induction chemotherapy or radiolabeled antibody

• Must be ineligible for autologous transplantation due to one of the following criteria:

  • Prior autologous transplantation
  • Inadequate autologous stem cell harvest
  • Inability to withstand a myeloablative preparative regimen
  • Clinically aggressive/high-risk disease

• No evidence of progressive disease by imaging modalities or biopsy

  • Persistent PET activity is not an exclusion criteria in the absence of CT changes indicating progression
• No available 5-6/6 HLA-A, -B, -DRB1 matched sibling donor
• No active CNS malignancy

• Umbilical cord blood graft must match at 4-6 HLA-A, B, DRB1 antigens

  • Antigen mismatches of 0-2 at the A, B, or DRB1 loci allowed
  • Each unit must be a 4-6 HLA-A, B, DRB1 antigen match to each other AND a 4-6 antigen match to the recipient

PATIENT CHARACTERISTICS:

• No decompensated congestive heart failure
• No uncontrolled arrhythmia
• LVEF ≥ 35%
• DLCO > 30% of predicted
• AST and ALT < 5 times upper limit of normal (ULN)
• Bilirubin < 3 times ULN

• Creatinine ≤ 2.0 mg/dL (adults) OR creatinine clearance > 40 mL/min (pediatrics)

  • Adults with creatinine > 1.2 mg/dL or a history of renal dysfunction must have creatinine clearance > 40 mL/min
• Karnofsky performance status (PS) 60-100% OR
• Lansky PS 50-100% (pediatrics)
• Prior mold infection (e.g., Aspergillus) must be cleared by Infectious Disease after receiving 1 month of treatment and infection controlled
• Not pregnant or nursing
• No evidence of HIV infection or known HIV-positive serology
• No current active serious infection
• Negative pregnancy test
• Fertile patients must use effective contraception

PRIOR CONCURRENT THERAPY:

• See Disease Characteristics
• At least 3 months since prior myeloablative transplant if this is the patient's second bone marrow transplant
• At least 3 months since multiagent chemotherapy (patients allowed provided they receive anti-thymocyte globulin during the preparative regimen)
• No oxygen requirements