Umbilical Cord Blood Stem Cell Transplant in Treating Patients With Hematologic Cancer or Other Disease

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