Study: NCT00972101

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Melphalan
Description: 140 mg/m\^2 by vein over 30 minutes as a single dose on Day -8

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Thiotepa
Description: 10 mg/kg by vein over 4 hours as a single dose on Day -7

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Fludarabine
Description: 40 mg/m\^2 by vein over about 30 minutes 1 time each day on Days -6 through -3.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Rituximab
Description: Regimen 1:~375 mg/m\^2 may be given by vein over 4 - 6 hours on Day -9 if needed~Regimen 2:~375 mg/m\^2 may be given by vein over 4 - 6 hours on Day -8 if needed

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Rituximab
Description: Regimen 1:~375 mg/m\^2 may be given by vein over 4 - 6 hours on Day -9 if needed~Regimen 2:~375 mg/m\^2 may be given by vein over 4 - 6 hours on Day -8 if needed

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Etoposide
Description: 60 mg/m\^2 by vein over 1-2 hours as a single dose on Day -3.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Anti-thymocyte globulin (ATG)
Description: Regimen 1:~1.25 and 1.75 mg/kg by vein over 4-6 hours on the Days -4 and -3.~Regimen 2:~0.5, 1.0 and 1.5 mg/kg by vein over 4-6 hours on respective Days -3, -2, and -1.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Anti-thymocyte globulin (ATG)
Description: Regimen 1:~1.25 and 1.75 mg/kg by vein over 4-6 hours on the Days -4 and -3.~Regimen 2:~0.5, 1.0 and 1.5 mg/kg by vein over 4-6 hours on respective Days -3, -2, and -1.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Mycophenolate Mofetil (MMF)
Description: 15 mg/kg pills twice a day starting on day -3, and continued until Day 100+ after transplant (1 gram may be given by vein if necessary).

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Mycophenolate Mofetil (MMF)
Description: 15 mg/kg pills twice a day starting on day -3, and continued until Day 100+ after transplant (1 gram may be given by vein if necessary).

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Tacrolimus
Description: 0.03 mg/kg by vein Day -2 as 24 hour continuous infusion for several weeks. After stem cell transplant, tacrolimus given by mouth 2 times a day for up to 6 months.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Tacrolimus
Description: 0.03 mg/kg by vein Day -2 as 24 hour continuous infusion for several weeks. After stem cell transplant, tacrolimus given by mouth 2 times a day for up to 6 months.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Cord Blood Infusion
Description: Cord blood infusion of larger portion through vein using Central Venous Catheter (CVC) on Day 0.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Cord Blood Infusion
Description: Cord blood infusion of larger portion through vein using Central Venous Catheter (CVC) on Day 0.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: G-CSF
Description: 5 mcg/kg day subcutaneously (may round up to the next vial) beginning on day +1 and continuing till absolute neutrophil count is \> 2.5 x 10e\^9/L.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: G-CSF
Description: 5 mcg/kg day subcutaneously (may round up to the next vial) beginning on day +1 and continuing till absolute neutrophil count is \> 2.5 x 10e\^9/L.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Ex vivo expanded T cell Infusion
Description: Infusion by vein of treated cord blood beginning dose of 1 x 10e\^5 T cells/kg on Day 14+.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Ex vivo expanded T cell Infusion
Description: Infusion by vein of treated cord blood beginning dose of 1 x 10e\^5 T cells/kg on Day 14+.