This is a phase II trial using a non-myeloablative cyclophosphamide/ fludarabine/total body
irradiation (TBI) preparative regimen followed by a related or unrelated donor stem cell
infusion. The primary objective is to evaluate rates of acute graft-versus-host disease
(GVHD) grades II-IV and chronic GVHD with an updated GVHD prophylaxis of tacrolimus and
mycophenolate mofetil (MMF) with a non-myeloablative preparative regimen in persons with
hematologic malignancies.