Group A (adults): 1. Adult patients affected by: - Acute leukemia (AML, ALL) defined as: - Acute Myeloid Leukemia (AML): - High risk AML in CR1; any adverse genetic abnormality, secondary or therapy related AML excluding good risk genetic abnormalities - Chemo-refractory relapse (MRD+) - ≥ CR2 - Acute Lymphoblastic Leukemia (ALL): - Chemo-refractory relapse (MRD+) - High risk ALL in CR1; Philadelphia (like) or any poor risk feature - ≥ CR2 - Acute leukemia of ambiguous lineage: - ≥ CR1 with a minimal residual disease (MRD) <5% (flow cytometry, molecular and/or cytogenetics accepted) - Myelodysplastic Syndrome (MDS) with least one of the following: - Revised International Prognostic Scoring System risk score of intermediate or higher at the time of transplant evaluation. - Life-threatening cytopenia. - Karyotype or genomic changes that indicate high risk for progression to acute myelogenous leukemia, including abnormalities of chromosome 7 or 3, mutations of TP53, or complex or monosomal karyotype. - Therapy related disease or disease evolving from other malignant processes. 2. Patient eligible for a T-depleted allogeneic HSCT 3. Age ≥ 18y and clinical condition compatible with allogeneic stem cell transplantation 4. Karnofsky index ≥ 70% prior to conditioning regimen 5. Patients with normal organ function prior to conditioning regimen Group B (pediatrics): 1. Pediatric patients affected by acute leukemia defined as: - Acute Myeloid Leukemia (AML): - High risk AML in CR1; any adverse genetic abnormality, secondary or therapy related AML excluding good risk genetic abnormalities, - Chemo-refractory relapse (MRD+) - ≥ CR2 - Acute Lymphoblastic Leukemia (ALL): - Chemo-refractory relapse (MRD+) - High risk ALL in CR1; Philadelphia (like) or any poor risk feature - ≥ CR2 - Acute leukemia of ambiguous lineage: - ≥ CR1 with a minimal residual disease (MRD) <5% (flow cytometry, molecular and/or cytogenetics accepted) 2. Patient eligible for a T-depleted allogeneic HSCT 3. Age < 18y at the time of inclusion 4. Absence of a matched sibling donor (MSD) 5. Lansky ≥ 70% / Karnofsky performance status ≥ 70% prior to conditioning regimen 6. Patients with normal organ function prior to conditioning regimen

Groups A and B: 1. Use of an HLA matched Cord Blood (8/8 allele matched) or haploidentical donor 2. Prior therapy with allogeneic stem cell transplantation 3. Treatment with another cellular therapy within one month before inclusion