DISEASE CHARACTERISTICS:

• Diagnosis of hematological malignancy, meeting any of the following criteria:

  • Acute Myeloid Leukemia (AML)

    • High-risk complete remission (CR) 1 as evidenced by preceding myelodysplastic syndrome (MDS), high risk cytogenetics (e.g., monosomy 5 or 7) OR high-risk as defined by referring institution treatment protocol, ≥ 2 courses to obtain CR, erythroblastic or megakaryocytic leukemia, and ≥ CR2
    • All patients must be in CR as defined by hematologic recovery and < 5% blasts by morphology within the bone marrow and a cellularity of ≥ 15%
    • Patients in which adequate marrow/biopsy specimens can not be obtained to determine remission status by morphologic assessment, but have fulfilled criteria of remission by flow cytometry, recovery of peripheral blood counts with no circulating blasts, and/or normal cytogenetics (if applicable) may still be eligible and must be discussed with the Principal Investigator
    • Patients < 21 years of age are eligible if M2 marrow is present with ≤ 25% blasts in marrow after having failed at least 1 course of chemotherapy

  • Acute lymphoblastic leukemia

    • High-risk CR1 [e.g., t(9;22), t(1;19), t(4;11) or other MLL rearrangements, or haplodiploidy]
    • Required > 1 course to obtain CR
    • In ≥ CR2
    • All patients must be in CR as defined by hematologic recovery and < 5% blasts by morphology within the bone marrow and a cellularity of ≥ 15%
    • Patients in which adequate marrow/biopsy specimens can not be obtained to determine remission status by morphologic assessment, but have fulfilled criteria of remission by flow cytometry, recovery of peripheral blood counts with no circulating blasts, and/or normal cytogenetics (if applicable) may still be eligible and must be discussed with the Principal Investigator

  • Chronic myelogenous leukemia, excluding refractory blast crisis

    • Patients must have failed or be intolerant to imatinib mesylate to be eligible in first chronic phase (CP1)
  • Advanced myelofibrosis
  • MDS in intermediate-2 by International Prognostic Scoring System, high-risk (i.e., refractory anemia with excess blasts [RAEB] or RAEB in transformation), refractory anemia with severe pancytopenia, or high-risk cytogenetics (blasts must be < 10% by a representative bone marrow aspirate morphology)
  • Lymphoblastic lymphoma, Burkitt lymphoma, or other high-grade non-Hodgkin lymphoma (NHL) after initial therapy if stage III/IV in partial remission (PR) 1 or after progression if stage I/II < 1 year (stage III/IV patients are eligible after progression in CR/PR)

  • Chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), marginal zone B-cell lymphoma, lymphoplasmacytic lymphoma, or follicular lymphoma that has progressed after at least two different prior therapies

    • Patients with bulky disease (nodal mass > 5 cm) should be considered for debulking chemotherapy before transplant
  • Patients with mantle cell lymphoma or prolymphocytic leukemia are eligible after initial therapy in ≥ CR1 or ≥ PR1

  • Large cell NHL > CR2 and > PR2

    • Patients in CR2/PR2 with initial short remission (< 6 months) are eligible

  • Multiple myeloma beyond PR2

    • Patients with chromosome 13 abnormalities and first response lasting < 6 months or β-2 microglobulin > 3 mg/L may be eligible after initial therapy
• No chemotherapy-refractory large cell or high-grade NHL (i.e., progressive disease after > 2 salvage regimens)

• UCB graft matched at 4-6 HLA-A, -B, -DRB1 antigens with the recipient

  • May include 0-2 antigen mismatches at the A or B or DRB1 loci
  • If 2 UCB units are required to reach the target cell dose, each unit must be a 3-6 HLA-A, -B, -DRB1 antigen match to each other, as well as a 4-6 antigen match to the recipient

PATIENT CHARACTERISTICS:

• Karnofsky performance status (PS) 70-100% (adults) OR Lansky PS 50-100% (children)
• Creatinine < 2.0 mg/dL (adults) OR creatinine clearance > 60 mL/min (children)
• Not pregnant or nursing

• None of the following conditions or diseases:

  • Fulminant liver failure
  • Cirrhosis with evidence of portal hypertension or bridging fibrosis
  • Alcoholic hepatitis
  • Esophageal varices
  • History of bleeding esophageal varices, hepatic encephalopathy, or correctable hepatic synthetic dysfunction evidenced by prolongation of the prothrombin time
  • Ascites related to portal hypertension
  • Bacterial or fungal abscess
  • Biliary obstruction
  • Chronic viral hepatitis with total serum bilirubin > 3 mg/dL
  • Symptomatic biliary disease
• DLCO corrected > 50% normal
• Left ventricular ejection fraction > 45%
• No uncontrolled viral or bacterial infection at the time of study enrollment
• No active or recent (prior 6 months) invasive fungal infection without Infectious Disease consult and approval
• No history of HIV infection

PRIOR CONCURRENT THERAPY:

• At least 6 months since prior myeloablative transplantation (patients ≤ 18 years of age)
• No prior myeloablative allotransplantation or autologous transplantation (patients > 18 years of age)
• No more than 12 months since prior extensive alkylator therapy (6 months for alkylator therapy with extensive radiation)
• No prior Y-90 ibritumomab or I-131 tositumomab as part of salvage therapy