OBJECTIVES:
* Determine the response rate of patients with chronic myeloid leukemia, acute leukemia, lymphoma, myeloma, myelodysplasia, aplastic anemia, Fanconi's anemia, histiocytosis, hereditary immunodeficiency, or storage disorder treated with allogeneic umbilical cord and placental blood transplantation.
* Determine the toxicity of this regimen in these patients.
* Determine survival in these patients treated with this regimen.
* Determine the incidence of graft-versus-host disease in these patients treated with this regimen.
OUTLINE: Patients receive a standard preparative regimen for their disease. Following the preparative regimen patients undergo umbilical cord blood stem cell transplantation on day 0.
Patients are followed every 1-2 weeks for 6 months.
PROJECTED ACCRUAL: A total of 30 patients will be accrued for this study within 4-5 years.
