Administration of Off-the-Shelf, Expanded, Most Closely HLA Matched, Third Party Adenovirus Specific T Cells for Therapy of Adenovirus Related Disease in Immunocompromised Patients

Inclusion Criteria: * Immunocompromised patients. * English and non-English speaking patients. * Written informed consent and/or signed assent from patient, parent or guardian. * Negative pregnancy test in female patients of childbearing potential, defined as not post-menopausal for 12 months or no previous surgical sterilization. Women of child bearing potential must be willing to use an effective contraceptive measure while on study. * Patients age 1 year or older with asymptomatic adenovirus viremia defined as no symptoms of adenovirus disease and EITHER two positive and quantifiable qPCR tests taken one week apart or one single measurement with \>/= 1000 copies. * Patients age 1 year or older with criteria of probable or definitive adenoviral diseases as defined in Appendix A. * Willingness to comply with the study protocol requirements. Exclusion Criteria: * Patients receiving prednisone \> 0.1 mg/kg/day or equivalent at time of enrollment, or who have received anti-thymocyte globulin (ATG) within 14 days or have received donor lymphocyte infusion (DLI) or Campath within 28 days of enrollment. * Patients with other uncontrolled infections: For bacterial infections, patients must be receiving therapy and have no signs of progressing infection for 72 hours prior to enrollment. For fungal infections patients must be receiving anti-fungal therapy and have no signs of progressing infection for 1 week prior to enrollment. Progressing infection is defined as hemodynamic instability attributable to sepsis or new symptoms, worsening physical signs or radiographic findings attributable to infection. Persisting fever without other signs or symptoms will not be interpreted as progressing infection. * Active acute graft versus host disease (GVHD) grade \>= 2.