Conditioning SCID Infants Diagnosed Early

The investigators want to study if lower doses of chemotherapy will help babies with SCID to achieve good immunity with less short and long-term risks of complications after transplantation. This trial identifies babies with types of immune deficiencies that are most likely to succeed with this approach and offers them transplant early in life before they get severe infections or later if their infections are under control. It includes only patients receiving unrelated or mismatched related donor transplants. The study will test if patients receiving transplant using either a low dose busulfan or a medium dose busulfan will have immune recovery of both T and B cells, measured by the ability to respond to immunizations after transplant. The exact regimen depends on the subtype of SCID the patient has. Donors used for transplant must be unrelated or half-matched related (haploidentical) donors, and peripheral blood stem cells must be used. To minimize the chance of graft-versus-host disease (GVHD), the stem cells will have most, but not all, of the T cells removed, using a newer, experimental approach of a well-established technology. Once the stem cell transplant is completed, patients will be followed for 3 years. Approximately 9-18 months after the transplant, vaccinations will be administered, and a blood test measuring whether your child's body has responded to the vaccine will be collected.

Inclusion Criteria: 1\. Infants with SCID, either typical or leaky or Omenn syndrome. 1. Typical SCID is defined as either of the following * Absence or very low number of T cells (CD3+ T cells \80% of CD3+ or CD4+ T cells are CD62L negative AND/OR \>50% of CD3+ or CD4+ T cells express HLA-DR (\