Treatment of Single or Double Umbilical Cord Trans + Graft-versus-host Disease (GVHD) Prophylaxis w/ Tacrolimus & Mycophenolate Mofetil

OBJECTIVES: Primary * To determine the safety (as assessed by the day 100 non-relapse mortality) and feasibility of single or double umbilical cord stem cell transplantation in patients with hematological malignancies receiving graft-versus-host disease (GVHD) prophylaxis comprising tacrolimus and mycophenolate mofetil (MMF). Secondary * To assess sustained donor engraftment, neutrophil recovery, platelet recovery, incidence and severity of acute graft-versus-host disease (GVHD) and chronic GVHD, relapse rate, 100-day all-cause mortality, overall survival, and immune reconstitution after single or double umbilical cord stem cell transplantation in patients with hematologic malignancies receiving graft-versus-host disease(GVHD) prophylaxis comprising tacrolimus and mycophenolate mofetil (MMF). OUTLINE: * Conditioning: Patients receive myeloablative or reduced-intensity conditioning regimen according to age and prior treatment. * Myeloablative conditioning (pediatric patients): Patients undergo total-body irradiation on days -7 to -4, and receive cyclophosphamide IV over 1 hour on days -3 and -2, methylprednisolone IV twice daily on days -3 to -1, and anti-thymocyte globulin IV over 4 hours on days -3 to -1. * Myeloablative conditioning (adult patients 18-40 years old): Patients receive fludarabine phosphate IV over 30 minutes on days -6 to -4, cyclophosphamide IV over 1 hour on days -5 and -4, and undergo total-body irradiation on days -3 to -1. * Reduced-intensity conditioning (patients over 40 and no more than 50 years old OR deemed ineligible for above myeloablative conditioning regimen due to previous treatment): Patients receive fludarabine phosphate IV over 30 minutes on days -6 to -2 and cyclophosphamide IV over 1 hour on day -6 and undergo total-body irradiation on day -1. * Umbilical cord blood transplantation (UCBT): All patients undergo single- or double-unit umbilical cord blood transplantation (UCBT)on day 0. * Graft-versus-host disease prophylaxis: Patients receive tacrolimus IV continuously or orally twice daily on days -2 to 180 followed by a tapering and mycophenolate mofetil IV or orally twice daily on days 0-100 followed by a tapering over the next 3 months. Patients also receive filgrastim (G-CSF) IV or subcutaneously beginning on day 0\* and continuing until blood counts recover. NOTE: \*In adult patients receiving a reduced intensity transplant, G-CSF will be started when the total white cell count falls below 2.5 x 109/L. After completion of study treatment, patients are followed monthly for 1 year and then every 2-4 months thereafter.