Inclusion Criteria:

          -  Malignant conditions for which CD34+ selected, T-cell depleted allogeneic
             hematopoietic stem cell transplantation is indicated such as:

        AML in 1st remission - for patients whose AML does not have 'good risk' cytogenetic
        features (i.e. t 8;21, t15;17, inv 16).

          -  Secondary AML in 1st remission

          -  AML in 1st relapse or > 2nd remission

          -  ALL/LL in 1st remission clinical or molecular features indicating a high risk for
             relapse; or ALL > 2nd remission

          -  CML failing to respond to or not tolerating Imatinib, dasatinib, or nilotinib in first
             chronic phase of disease; or CML in accelerated phase or second chronic phase.

          -  Non-Hodgkins lymphoma with chemoresponsive disease in any of the following categories:
             a) intermediate or high grade lymphomas who have failed to achieve a first CR or have
             relapsed following a 1st remission who are not candidates for autologous transplants.

          -  any NHL in remission which is considered not curable with chemotherapy alone and not
             eligible/appropriate for autologous transplant. Myelodysplastic syndrome (MDS):
             RA/RCMD with high risk cytogenetic features or transfusion dependence, RAEB-1 and
             RAEB-2 and Acute myelogenous leukemia (AML) evolved from MDS, who are not eligible for
             transplantation under protocol IRB 08-008.

          -  Chronic myelomonocytic leukemia: CMML-1 and CMML-2.

          -  Other rare lethal disorders of Hematopoiesis and Lymphopoiesis for which a T-cell
             depleted transplant is indicated (e.g. hemophagocytic lymphohistiocytosis; refractory
             aplastic anemia or conjugated cytopenias; non-SCID lethal genetic immunodeficiencies
             such as Wiskott Aldrich Syndrome, CD40 ligand deficiency, ALPS).

          -  Patients may be of either gender and of any racial or ethnic background.

          -  Patients must have a Karnofsky (adult) or Lansky (pediatric) Performance Status > 70%.

          -  Patients must have adequate organ function measured by:

        Cardiac: asymptomatic or if symptomatic then LVEF at rest must be > 50% and must improve
        with exercise.

          -  Hepatic: < 3x ULN ALT and < 2.0x ULN total serum bilirubin, unless there is congenital
             benign hyperbilirubinemia.

          -  Renal: serum creatinine <1.2 mg/dl or if serum creatinine is outside the normal range,
             then CrCl > 40 ml/min (measured or calculated/estimated)

          -  Pulmonary: asymptomatic or if symptomatic, DLCO > 50% of predicted (corrected for
             hemoglobin)

          -  Each patient must be willing to participate as a research subject and must sign an
             informed consent form.

        Exclusion Criteria:

          -  Female patients who are pregnant or breast-feeding

          -  Uncontrolled viral, bacterial or fungal infection

          -  Patient seropositive for HIV-I/II; HTLV -I/II

          -  Presence of leukemia in the CNS.

        Donor Inclusion Criteria:

          -  Each donor must meet criteria outlined by institutional policies

          -  Donor must have adequate peripheral venous catheter access for leukapheresis or must
             agree to placement of a central catheter.

        Donor Exclusion Criteria:

          -  Evidence of active infection (including urinary tract infection, or upper respiratory
             tract infection), viral hepatitis exposure (on screening), unless only HBS Ab+ and HBV
             DNA negative, or serologic evidence of exposure or infection with HIV-I/II or
             HTLV-I/II

          -  If donors do not meet institutional guidelines, exclusion will be considered.