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Fludarabine Phosphate, Cyclophosphamide, Thiotepa, and Total Body Irradiation Before Donor Umbilical Cord Blood Transplant in Treating Patients with Blood Cancer

Trial Status: complete

This phase II trial studies how well fludarabine phosphate, cyclophosphamide, thiotepa, and total body irradiation before donor umbilical cord blood transplant work in treating patients with blood cancer. Giving chemotherapy and total body irradiation, before donor umbilical cord blood transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and cancer 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 (called graft-versus-host disease). Giving cyclosporine and mycophenolate mofetil before the transplant may stop this from happening.