Rituximab (Rituxan) for the Prevention of EBV-LPD Epstein Barr Virus (EBV) Lymphoproliferative Disorder Post T Cell Depleted Unrelated and HLA Mis-matched Related HSCT

Inclusion Criteria: * Patient must be a recipient of aT cell depleted unrelated or HLA mis-matched related HSCT for the treatment of a malignancy or immunodeficiency disease. * Patients must have an ANC \> or = to 1500 cells/ul on the day of first treatment. * Patients with acute or chronic leukemia, or MDS prior to transplant must be in remission defined as \<5% blasts in the bone marrow. * Patient with must be in remission. * Patient must be Hepatitis B surface antigen negative pre transplant. * Patients must have adequate cardiac function defined as a left ventricular ejection fraction at rest of \>50% documented pre-transplant. * Patient may be of either gender and of any ethnic background. * Patient may be of any age. There is no upper age restriction. * Patients or their guardians must be able to understand the nature and risk of the proposed study and be able to sign consent. Exclusion Criteria: * Karnofsky score \<70% * Female patients who are pregnant or lactating. * Evidence of EBV-LPD or circulating EBV copy number \>1000. * Active uncontrolled bacterial or fungal infection. * Prior history of Hepatitis B infection or Hepatitis B surface antigen positivity pre transplant. * HIV-1,2 sero-positive patients. * Patients or guardians not signing informed consent. * Patients with prior allergic reaction to Rituximab or other murine monoclonal antibody. * Patients taking other investigational agents under another protocol unless discussed and approved in advance by Genentech and the IDEC Therapeutic Director.