Busulfan, Antithymocyte Globulin, and Fludarabine Followed By a Donor Stem Cell Transplant in Treating Young Patients With Blood Disorders, Bone Marrow Disorders, Chronic Myelogenous Leukemia in First Chronic Phase, or Acute Myeloid Leukemia in First Remission

DISEASE CHARACTERISTICS:

* Diagnosis of one of the following hematopoietic disorders:

  * Severe aplastic anemia with marrow aplasia (i.e., absolute neutrophil count \< 500/mm\^3, platelet and/or red blood cell transfusion dependent), meeting 1 of the following criteria:

    * Closely matched related donor
    * Unresponsive to immunosuppressive therapy within 3 months after follow-up AND alternative matched unrelated donor available
  * Congenital marrow failure syndrome, including any of the following:

    * Primary red blood cell aplasia (Diamond-Blackfan syndrome)
    * Congenital neutropenia (Kostmann's syndrome)
    * Amegakaryocytic thrombocytopenia
  * Hemoglobinopathy including any of the following:

    * β-thalassemia major
    * Sickle cell anemia
  * Severe immunodeficiency disease including any of the following:

    * Chediak-Higashi disease
    * Wiskott-Aldrich syndrome
    * Combined immunodeficiency disease (Nezelof's)
    * Hyperimmunoglobulin M syndrome
    * Bare lymphocyte syndrome
  * Other stem cell defects (e.g., osteopetrosis)
  * Chronic myelogenous leukemia in first chronic phase

    * Not eligible for other ongoing phase II/III studies
  * Acute myeloid leukemia in first remission

    * Not eligible for other ongoing phase II/III studies
  * Inborn errors of metabolism
* No severe combined immunodeficiency disorder
* Available donor, meeting 1 of the following criteria:

  * Related donor matched by high resolution DNA typing at both HLA Drβ1 alleles and ≤ 1 mismatch at the 4 HLA-A and -B alleles
  * Unrelated donor, meeting one of the following criteria:

    * Bone marrow matched by high resolution DNA typing at both HLA Drβ1 alleles and ≤ 1 mismatch by high resolution DNA typing at the 4 HLA-A and -B alleles
    * Umbilical cord blood matched at 4/6 HLA-A, -B, and Drβ1 alleles by high resolution typing with ≥ 1 Drβ1 match and ≥ 3 X 10\^7 cells/kg body weight of recipient

PATIENT CHARACTERISTICS:

* See Disease Characteristics
* No active bacterial, viral, or fungal infection
* Cardiac shortening fraction ≥ 27%
* Creatinine clearance ≥ 60 mL/min
* DLCO ≥ 60% of predicted (corrected for anemia/lung volume)

PRIOR CONCURRENT THERAPY:

* See Disease Characteristics