UCB Transplant for Hematological Diseases Using a Non Myeloablative Prep

Inclusion Criteria: * Age, Performance Status, and Graft Criteria * \<70 years of age with no matched 5/6 or 6/6 sibling donor - patients ≥ 70 and ≤ 75 years of age may be eligible if they have a Co-Morbidity score ≤ 2 (http://www.qxmd.com/calculate-online/hematology/hct-ci) * Karnofsky score ≥ 70% (≥ 16 years) or Lansky score ≥ 50 (\< 16 years) * UCB graft selected according to current University of Minnesota umbilical cord blood graft selection algorithm * Eligible Diseases All diseases listed below are advanced hematologic malignancies not curable by conventional chemotherapy. Responses to conventional treatment range from zero to 30% but are typically short lived. * Acute Leukemias: Must be in remission by morphology (\<5% blasts). Note cytogenetic relapse or persistent disease without morphologic relapse is acceptable. Also a small percentage of blasts that is equivocal between marrow regeneration vs. early relapse are acceptable provided there are no associated cytogenetic markers consistent with relapse. * Acute Myeloid Leukemia (AML) and related precursor neoplasms: 2nd or greater complete remission (CR); first complete remission (CR1) in patients \> 60 years old; CR1 in ≤ 60 years old that is NOT considered as favorable-risk. Favorable risk AML is defined as having one of the following: * t(8,21) without cKIT mutation * inv(16) or t(16;16) without cKIT mutation * Normal karyotype with mutated NPM1 and wild type FLT-ITD * Norma…