Unrelated Cord Blood (UCB) transplant in children is a viable stem cell transplant modality for patients with leukemia and myelodysplasia. UCB is now considered "Standard Of Care" in cases where a suitable living bone marrow donor is not available. The survival of UCB is similar to Matched Unrelated Marrow Transplant. This study is considered "Research" since UCB is not a licensed product and requires investigational new drug (IND). THERE ARE NO SPECIFIC RESEARCH QUESTIONS IN THIS PROTOCOL. This protocol merely provides UCB as a stem cell treatment modality to pediatric patients who may require it after a conditioning regimen that excludes Total Body Irradiation.