DISEASE CHARACTERISTICS:

• Histologically confirmed diagnosis of 1 of the following:

  • Acute myeloid leukemia meeting the following criteria:

    • M0-M7 histologic subtypes by French-American-British classification
    • Previously treated disease

    • Meets 1 of the following criteria:

      • Persistent disease as evidenced by 5-30% persistent blasts in bone marrow after induction or salvage therapy
      • In second or subsequent complete remission (CR)

      • In first CR with 1 of the following high-risk features:

        • Philadelphia chromosome present
        • Noncore-binding factor type of chromosomal abnormalities

  • Myelodysplastic syndromes with 1 of the following International Prognostic Scoring System (IPSS) scores:

    • Intermediate-1
    • Intermediate-2
    • High-risk score with transfusion dependence

  • Chronic myelogenous leukemia meeting 1 of the following criteria:

    • In accelerated or blastic phase
    • Failed prior imatinib mesylate therapy

  • Acute lymphoblastic leukemia meeting 1 of the following criteria:

    • In first CR with any of the following high-risk features:

      • Philadelphia chromosome present
      • Translocation t(4;11) present
      • WBC > 30,000/mm³ (adult patients)
      • More than 4 weeks from initiation of treatment was required to achieve CR (adult patients)
      • DNA index of near haploid (N=23 chromosomes) (pediatric patients)
    • In second or subsequent CR
    • Persistent disease as evidenced by 5-20% persistent blasts in bone marrow after induction or salvage therapy

  • Hodgkin's or non-Hodgkin's lymphoma meeting the following criteria:

    • Recurrent or refractory disease
    • Tumor ≤ 5 cm in diameter

  • Myeloma or plasma cell neoplasm meeting 1 of the following staging criteria:

    • Stage III at presentation

    • Stage I-II at presentation

      • Not responding OR progressed after first-line therapy
  • Chronic lymphocytic leukemia or Waldenstrom's macroglobulinemia with refractory or progressive disease after first-line therapy
• No 5-6/6 HLA-matched related or 7-8/8 HLA-matched unrelated marrow or peripheral blood stem cell donor available
• No single 4-6/6 HLA-A, -B, or -DRB1-matched umbilical cord blood unit ≥ 3.5 x 10^7 nucleated cells/kg available

PATIENT CHARACTERISTICS:

• ECOG performance status (PS) 0-2 OR Karnofsky or Lansky PS 70-100%
• Not pregnant
• Fertile patients must use effective contraception prior to and during study participation
• HIV negative
• Bilirubin < 3.0 mg/dL
• AST and ALT ≤ 3 times upper limit of normal
• Creatinine < 2.0 mg/dL OR creatinine clearance > 50 mL/min
• Cardiac ejection fraction > 50% by echocardiogram OR shortening fraction > 27%
• No uncontrolled symptomatic congestive heart failure
• No unstable angina pectoris
• No cardiac arrhythmia
• FEV_1 > 50% of normal
• Forced vital capacity > 50% of normal
• DLCO normal
• Oxygen saturation > 92% on room air (for patients < 5 years of age)
• No history of allergic reactions attributed to compounds of similar chemical or biological composition to busulfan and fludarabine phosphate
• No ongoing or active infection
• No psychiatric illness or social situation that would preclude study compliance
• No other uncontrolled illness

PRIOR CONCURRENT THERAPY:

• See Disease Characteristics
• At least 4 weeks since prior and no concurrent surgery
• At least 4 weeks since prior and no other concurrent investigational or commercial agents or therapies for the malignancy, including chemotherapy, biologic therapy, or radiotherapy