Biparental HLA Haplotype Disparate T-cell Depleted Transplants for Patients Lacking an HLACompatible Donor

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.