Inclusion Criteria:

          1. Signed informed consent

          2. Patients with one of the life-threatening hematological malignancies:

               -  Acute lymphocytic leukemia (ALL) in CR1 with high-risk features including adverse
                  cytogenetics such as t(9;22), t(1;19), t(4;11), or MLL gene rearrangements;
                  greater than 1 cycle to achiever remission or with persistent MRD; ALL in second
                  or greater remission with or without MRD. Acute myeloid leukemia (AML) in CR1
                  with high-risk features defined as: Greater than 1 cycle of induction therapy
                  required to achieve remission; Preceding myelodysplastic syndrome (MDS) or
                  myeloproliferative disease; Presence of FLT3 mutations or internal tandem
                  duplications; FAB M6 or M7 classification; Adverse cytogenetics, -5, del 5q, -7,
                  del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8 [> 3 abnormalities];

               -  AML in second or greater remission, primary induction failure and patients with
                  relapsed disease;

               -  Advanced chronic myeloid leukemia (CML) who have progressed to blast phase or
                  accelerated phase and are in need of a transplant and do not have an HLA matched
                  donor;

               -  MDS with IPSS intermediate-2 or higher or therapy-related MDS.Hodgkin lymphoma or
                  Non-Hodgkin lymphoma (NHL): relapsed disease where remission duration is less
                  than 1 year, relapse after previous autologous transplant, or failure to achieve
                  CR with chemotherapy.

          3. Age ≥ 18 years and ≤ 65 years

          4. Deemed eligible for allogeneic stem cell transplantation

          5. Lack of suitable conventional donor (i.e. 8/8 related or unrelated donor) or presence
             of rapidly progressive disease not permitting time to identify an unrelated donor

          6. HLA typing will be performed at high resolution (allele level) for the HLA-A, -B, Cw,
             and DRBl loci

               -  A minimum genotypic identical haplotype match of 4/8 is required

               -  The donor and recipient must be identical, as determined by high resolution
                  typing, at least one allele of each of the following genetic loci: HLA-A, HLA-B,
                  HLA-Cw, and HLA- DRB1

          7. Subjects with adequate organs function as measured by:

               -  Cardiac: Left ventricular ejection fraction at rest must be >45%

               -  Pulmonary: FEV 1, FVC, DLCO (diffusion capacity) > 50% predicted (corrected for
                  hemoglobin); or O2 saturation > 92% on room air

               -  Hepatic: Direct bilirubin ≤ 3 x upper limit of normal (ULN), or AST/ALT ≤ 5 x ULN

               -  Renal: Serum creatinine within normal range for age or creatinine clearance, or
                  with a recommended GFR ≥ 50 mL/min/1.73m2

          8. Performance status: Karnofsky ≥ 80%

        Exclusion Criteria:

          1. HLA 8/8 allele matched (HLA-A,-B,-Cw,-DRBl) related or unrelated donor able to donate;

          2. Autologous hematopoietic stem cell transplant ≤ 3 months prior to enrollment;

          3. Prior allogeneic transplantation;

          4. Active CNS involvement by malignant cells (less than 2 months from the conditioning);

          5. Current uncontrolled bacterial, viral or fungal infection (currently taking medication
             with evidence of progression of clinical symptoms or radiologic findings); the PI is
             the final arbiter of this criterion;

          6. Positive HIV serology or viral RNA (≥ Grade III per CTCAE criteria);

          7. Pregnancy (positive serum or urine βHCG test) or breast-feeding;

          8. Fertile men or women unwilling to use effective forms of birth control or abstinence
             for a year after transplantation;

          9. Bovine product allergy.

         10. Severe obesity (patient's weight is >/= 1.5x the donor weight).