To evaluate if HLA-mismatched, unrelated-donor umbilical cord blood stem and progenitor cell units (UCBU) offered a clinically acceptable alternative to matched unrelated-donor allogeneic bone marrow for transplantation with 180-day disease free survival as the endpoint. HLA typing was performed using DNA-base high resolution methods to determine HLA alleles. Patients with "true" HLA 3/6 and 4/6 matches were evaluated. In addition, a separate study in adults addressed the problem of limited cell dose and engraftment failure. The study was not planned as a randomized comparative clinical trial. Instead, it is a phase II/III efficacy study.