P3 Study of Umbilical Cord Blood Cells Expanded With MPCs for Transplantation in Patients With Hematologic Malignancies

Inclusion Criteria: * Patient must have one of the following: * Acute myelogenous leukemia (AML) in complete morphological remission at study screening (Complete Remission with Incomplete Platelet Recovery (CRp) acceptable). * Acute lymphoblastic leukemia (ALL) in complete morphological remission at study screening (Complete Remission with Incomplete Platelet Recovery (CRp) acceptable). * Non-Hodgkin's lymphoma (NHL): High risk subjects with responsive disease after first relapse. High risk includes those with Burkitt's Lymphoma and those with extensive marrow involvement at diagnosis-precluding autologous transplant. * Hodgkin's disease: High risk subjects with responsive disease after first relapse. * Minimum Karnofsky Scale * Subject must weigh at least 20 kg * Up to 65 years of age * Adequate major organ system function Exclusion Criteria: * Pregnancy and/or lactating * Suitable, 6/6 HLA matched related sibling donor available * Previous participation in a stem cell study within last 30 days