Brief Summary: RATIONALE: Giving chemotherapy, such as busulfan, fludarabine, and melphalan, before a donor umbilical cord blood stem cell transplant helps stop the growth of abnormal or cancer cells and prepares the patient's bone marrow for the stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil may stop this from happening. PURPOSE: This phase II trial is studying how well combination chemotherapy followed by a donor umbilical cord blood transplant works in treating infants with high-risk acute leukemia or myelodysplastic syndromes.

Detailed Description: OBJECTIVES: Primary * Determine the incidence of engraftment, defined as achieving donor-derived neutrophil count \> 500/mm³ by day 42, in infants with high-risk acute myeloid leukemia, acute lymphoblastic leukemia, or myelodysplastic syndromes treated with a non-irradiation containing myeloablative conditioning regimen comprising busulfan, fludarabine, and melphalan followed by double umbilical cord blood transplantation (UCBT) with two partially HLA-matched units. Secondary Objectives * Determine the incidence of transplant-related mortality (TRM) at 6 months after UCBT * Evaluate pattern of chimerism after double UCBT * Determine the incidence of platelet engraftment at 1 year after UCBT * Determine the incidence of acute graft-versus-host disease (GVHD) grade II-IV and grade III-IV at day 100 after UCBT * Evaluate the developmental outcome after UCBT Transplant Related Objectives * Determine the incidence of chronic GVHD at 1 year after UCBT * Determine the survival and disease free survival at 1 and 2 years after UCBT * Determine the incidence relapse at 1 and 2 years after UCBT