The protocol aims include: assessing thymopoiesis in the allograft biopsy; assessing immunoreconstitution of complete DiGeorge syndrome subjects after postnatal allogeneic thymus transplantation; assessing minimally invasive methods of assessing thymopoiesis (flow cytometry and polymerase chain reaction (PCR); assessing pre-transplant T cells which do not proliferate in response to mitogens (focusing on NK-T cells); and, assessing thymus transplantation safety and toxicity.