Chemotherapy and Total-Body Irradiation Followed by Donor Umbilical Cord Blood Transplant, Cyclosporine, and Mycophenolate Mofetil in Treating Patients With Hematologic Cancer

DISEASE CHARACTERISTICS: * Diagnosis of a hematologic malignancy of 1 of the following types: * Acute myeloid leukemia (AML), meeting the following criteria: * In complete remission (CR) by morphology (\< 5% blasts in the bone marrow), as defined by 1 of the following: * In first CR (CR1) and meets ≥ 1 of the following high-risk criteria: * High-risk cytogenetics (e.g., those associated with myelodysplastic syndromes \[MDS\] or complex karotype) * Preceding MDS * More than 2 courses of therapy was required to obtain CR * In second or greater CR * No morphologic relapse * Cytogenetic relapse or persistent disease allowed * Acute lymphocytic leukemia (ALL), meeting the following criteria: * In CR, as defined by 1 of the following: * In CR1 and meets ≥ 1 of the following high-risk criteria: * Unfavorable high-risk cytogenetics \[t(9;22), t(1;19), t(4;11) or other MLL rearrangements\] * More than 1 course of therapy was required to obtain CR * In second or greater CR * No morphologic relapse or persistent disease * Chronic myelogenous leukemia (CML), excluding refractory blast crisis * Advanced myelofibrosis * Advanced myelodysplasia (blasts \< 10% \[otherwise need AML induction pre-transplant\]), meeting ≥ 1 of the following criteria: * Refractory anemia with excess blasts (RAEB) * RAEB in transformation * Refractory anemia with severe pancytopenia * High-ris…