Treatment of Hematologic Malignancies With Single-Unit or Double-Unit Cord Blood Transplantation

This is a non-randomized, phase II protocol to evaluate engraftment of cord blood after treatment with myeloablative conditioning of fludarabine, total body irradiation and cyclophosphamide. All patients will receive tacrolimus and mycophenolate mofetil as prophylaxis for graft-vs-host disease. Conditioning Regimen: * Days -10 to -7: Fludarabine 30mg/m2/day IV * Days -7 to -4: TBI 165 centigray BID * Days -3 to -2: Cyclophosphamide 40mg/kg/day IV Day 0: Infusion of Cord Blood Cells Graft-vs-Host Disease Prophylaxis * Day -1: Start tacrolimus 0.03mg/kg/day IV * Day 0: Start MMF 7.5mg/kg IV BID