DISEASE CHARACTERISTICS:

• Diagnosis of 1 of the following hematologic malignancies:

  • Acute myeloid leukemia (AML)

    • Disease in second or subsequent complete remission (CR)* OR in first CR* with high-risk features, as defined by 1 of the following:

      • Preceding myelodysplastic syndromes (MDS)
      • High-risk cytogenetics
      • Two or more courses of therapy required to obtain CR*
      • Erythroblastic or megakaryocytic leukemia
    • Very high-risk pediatric patients (< 21 years of age) are eligible provided M2 marrow ≤ 25% blasts after failing ≥ 1 course of prior chemotherapy

  • Acute lymphocytic leukemia (ALL)

    • Disease in second or subsequent CR* OR in first CR* with high-risk features, as defined by 1 of the following:

      • High-risk cytogenetics [t(9;22), t(1;19), t(4;11), or other MLL rearrangements]
      • More than 1 course of therapy required to obtain CR*

  • Chronic myelogenous leukemia

    • Not in refractory blast crisis
    • Must have failed or be intolerant to imatinib mesylate (for patients in first chronic phase)
  • Advanced myelofibrosis

  • MDS

    • Refractory anemia with severe pancytopenia or high-risk cytogenetics OR intermediate-2- or high-risk MDS by International Prognostic Scoring System, including any of the following:

      • Refractory anemia with excess blasts (RAEB)
      • RAEB in transformation
    • Blasts < 10% by a representative bone marrow aspirate morphology

  • Chronic lymphocytic leukemia

    • Disease progressed after ≥ 2 prior therapies
    • Patients with bulky disease (nodal mass > 5cm) may undergo debulking chemotherapy before transplantation

  • Prolymphocytic leukemia

    • Disease in first or subsequent CR or partial remission (PR) after initial therapy

  • Multiple myeloma, meeting 1 of the following criteria:

    • Beyond second PR

    • Completed initial therapy AND meets 1 of the following criteria:

      • Chromosome 13 abnormalities
      • First response lasted < 6 months
      • Beta-2 microglobulin > 3 mg/L

  • Any of the following non-Hodgkin's lymphoma (NHL)

    • Patients with small lymphocytic lymphoma, marginal zone B-Cell lymphoma, or follicular lymphoma must have disease progression after ≥ 2 prior therapies

      • Patients with bulky disease (nodal mass > 5cm) may undergo debulking chemotherapy before transplantation
    • Patients with lymphoplasmacytic lymphoma or mantle cell lymphoma must have undergone initial therapy and be in first or subsequent CR or PR

    • Patients with large cell NHL must meet both of the following criteria:

      • In second CR or PR with initial short remission (< 6 months) OR beyond second CR or PR
      • Not refractory to chemotherapy (i.e., progressive disease after > 2 salvage regimens)

    • Patients with lymphoblastic lymphoma, Burkitt's lymphoma, or other high-grade NHL must meet the following criteria:

      • Disease progressed within 1 year after initial therapy (for patients with stage I or II disease)
      • Competed initial therapy AND disease in first CR or PR (for patients with stage III or IV disease)
      • Not refractory to chemotherapy (i.e., progressive disease after > 2 salvage regimens) NOTE: *CR is defined by hematologic recovery AND marrow < 5% blasts by light microscopy with ≥ 15% cellularity (for patients with AML or ALL)

• Must have HLA matched unrelated umbilical cord blood (UCB) donor available

  • Must be 4/6, 5/6, or 6/6 HLA-A, -B, and -DRB1 matched

  • May use 1 or 2 units of UCB

    • If using 2 units, each unit must be 4/6 HLA-A, -B, and -DRB1 matched to both the patient and the other unit
• No HLA-identical related donor available NOTE: A new classification scheme for adult non-Hodgkin's lymphoma has been adopted by PDQ. The terminology of "indolent" or "aggressive" lymphoma will replace the former terminology of "low", "intermediate", or "high" grade lymphoma. However, this protocol uses the former terminology.

PATIENT CHARACTERISTICS:

• Karnofsky performance status (PS) 80-100% (for adult patients) OR Lansky PS 50-100% (for pediatric patients)
• Creatinine ≤ 2.0 mg/dL (for adult patients) OR creatinine clearance > 40 mL/min (for pediatric patients)
• AST and ALT ≤ 2 times upper limit of normal (ULN)
• Alkaline phosphatase ≤ 2 times ULN
• Bilirubin ≤ 2 times ULN
• DLCO_corr > 50% of normal
• LVEF ≥ 45%
• Not pregnant or nursing
• Negative pregnancy test
• Fertile patients must use effective contraception
• No Aspergillus or other mold infection within the past 30 days
• No history of HIV infection
• No other active infection at the time of study transplantation

PRIOR CONCURRENT THERAPY:

• See Disease Characteristics
• No prior alkylator therapy lasting > 12 months (6 months for alkylator therapy with extensive radiotherapy)
• More than 6 months since prior myeloablative transplantation (for patients ≤ 18 years of age)
• No prior myeloablative allogeneic or autologous transplantation (for patients > 18 years of age)
• No other prior extensive therapy
• No prior salvage therapy with yttrium Y 90 ibritumomab tiuxetan or iodine I 131 tositumomab