Pilot Study of Umbilical Cord Blood Transplantation in Adult Patient With Advanced Hematopoietic Malignancies

This study intends to demonstrate an engraftment rate of \>80% at day 100 post-transplantation and a transplant related mortality rate of \< or equal to 50%. A TRM of \>50% will be considered unacceptable. The present research will also: * Evaluate the toxicity of busulfan, fludarabine, and etoposide as preparative therapy prior to umbilical cord blood cell transplantation. * Evaluate neutrophil and platelet recovery following UCB transplantation. * Evaluate lineage-specific chimerism following transplantation and to assess the contribution of each individual CB unit to post-transplantation hematopoiesis. * Evaluate event free and overall survival. * Evaluate the incidence, severity and timing of acute and chronic GVHD following UCB transplantation.