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

RATIONALE: Giving chemotherapy and total-body irradiation before a donor umbilical cord blood transplant helps stop the growth of cancer and abnormal cells and helps stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving tacrolimus and mycophenolate mofetil before and after transplant may stop this from happening. PURPOSE: To look at the ability of umbilical cord blood cells from one or two unrelated donors to serve as a source of stem cells for people needing a bone marrow transplant.

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.