Cord Blood Transplant, Cyclophosphamide, Fludarabine, and Total-Body Irradiation in Treating Patients With High-Risk Hematologic Diseases

This trial is testing cord blood transplantation (using blood stem cells from donated umbilical cord blood) combined with a preparation regimen of cyclophosphamide, fludarabine, and total-body irradiation for people with high-risk blood cancers and other serious blood disorders. **You may be eligible if...** - You are between 6 months and 65 years old - You have a high-risk blood cancer or blood disorder such as: AML or ALL in remission, certain forms of leukemia, myelodysplastic syndrome, lymphoma, or inherited blood or immune disorders - Your cancer is in remission or at low blast count at the time of transplant - You do not have a fully matched related donor available (cord blood is used instead) **You may NOT be eligible if...** - Your leukemia is not in remission - You have serious organ dysfunction that would make transplant too risky - You have uncontrolled infection - You are pregnant or breastfeeding - Your overall health is too poor to tolerate the transplant procedure Talk to your doctor to see if this trial is right for you.