• Incidence of neutrophil recovery (absolute neutrophil count ≥500/µL for three consecutive days) . [ Time Frame: by day 42 ] [ Designated as safety issue: Yes ]
  

• Incidence of grade ≥3 regimen related toxicity . [ Time Frame: at day 100 ] [ Designated as safety issue: Yes ]
  
• Incidence of secondary graft failure at 100 days. [ Time Frame: 100 days ] [ Designated as safety issue: No ]
  
• Incidence of acute graft-versus-host disease (GVHD) [ Time Frame: at 100 days. ] [ Designated as safety issue: No ]
  
• Incidence of chronic GVHD . [ Time Frame: at one year ] [ Designated as safety issue: No ]
  
• Probability of survival . [ Time Frame: at one year ] [ Designated as safety issue: No ]
  
• Incidence of infections . [ Time Frame: at 100 days, 6 months and one year ] [ Designated as safety issue: No ]
  
• Immune reconstitution . [ Time Frame: at 100 days, 6 month and one year ] [ Designated as safety issue: No ]
  

Drug: Cyclophosphamide
Day -5 through Day -2, subjects will receive chemotherapy of Cyclophosphamide via central line (i.e. Hickman or Broviac).
Drug: Fludarabine
Day -5 through Day -2, subjects will receive chemotherapy of Fludarabine via central line (i.e. Hickman or Broviac).
Drug: ATG
Day -5 through Day -2, subjects will receive chemotherapy of ATG via central line (i.e. Hickman or Broviac).
Procedure: Total Body Irradiation
total body irradiation with thymic shielding will be given six days before the stem cells are given (day -6). Thymic shielding is done by placing a piece of lead on the chest during the irradiation treatment so that the irradiation beams do not go to the thymus.
Procedure: Bone Marrow Transplantation
Certain cancers can be treated by giving patients stem cells that come from someone else. This is called a stem-cell transplant. As part of the transplant process, patients receive high doses of chemotherapy and/or radiation to treat their underlying disease, such as cancer. As one of its effects, this treatment also kills the healthy stem cells that are already in the marrow. The transplant provides new stem cells for the patient from a healthy donor; that replace the bone marrow and allow the blood counts to recover.

Study Treatment: 1. If the subject is to receive total body irradiation with thymic shielding, it will be given six days before the stem cells are given (day -6). 2. Day -5 through Day -2, subjects will receive a chemotherapy regimen of Fludarabine, Cyclophosphamide, ATG, and Methylprednisone (a steroid used to help make sure the transplant "takes") via central line (i.e. Hickman or Broviac). On days -5 to -1, subjects will receive ATG and Methylprednisone. The methylprednisone will continue until about three weeks after transplant.3. Starting Day -3, subjects will be given cyclosporin A (CSA) therapy to help prevent graft-versus-host-disease. We will continue to give CSA until about six months after the transplant. 4. If the subject is receiving bone marrow or "peripheral" stem cells (cells collected from the donor's arm via a cell separator), on the day of transplantation, the stem cells taken from the donor will be put into a machine which will separate the lymphocytes (the cells that cause graft-versus-host disease [GVHD]) from the stem cells. If the subject is receiving an umbilical cord blood, the lymphocytes will not be removed because the risk of GVHD is not as high. Otherwise all patients will receive the same treatment. The stem cells are given as an infusion into the subject's existing catheter over 1-2 hours on day 0.5. On the day after transplant (day +1) subjects will be given G-CSF to stimulate the growth of the transplanted cells. 6. While receiving treatment and until the subject's blood counts recover he/she will have daily blood tests, and several bone marrow biopsies and aspirates. After recovery, subjects will be seen once a month for a health assessment and blood tests until at least 3 months after the cells have been infused. Additional blood tests or assessments may be done as medically indicated.

Inclusion Criteria:

• Patients must have a ≤1 antigen mismatched HLA-A, B, DRB1 unrelated donor or ≤1 antigen mismatched related (non-HLA-matched sibling) or ≤2 antigen mismatched unrelated UCB donor.
• Patients with FA must have aplastic anemia (AA), myelodysplastic syndrome without excess blasts, or high risk genotype.
• Adequate major organ function.
• Women of child-bearing age must be using adequate birth control and have a negative pregnancy test.

Exclusion Criteria:

• Available HLA-genotypically identical related donor.
• Refractory anemia with excess blasts, or leukemia.
• Active CNS leukemia at time of HSCT.
• History of squamous cell carcinoma of the head/neck/cervix within 2 years of HSCT.
• Pregnant or lactating female.
• Prior radiation therapy that prevents further TBI.
• Patients with advanced MDS (.i.e. RAEB or RAEBt or acute leukemia) will be excluded from this study