Study Evaluating the Safety and the Efficacy of Human T Lymphoid Progenitor (HTLP) Injection to Accelerate Immune Reconstitution After Umbilical Cord Blood (UCB) Transplantation in Adult Patients With Hematologic Malignancies (HTLP-ONCO)

Inclusion Criteria: * Adult patients (≥ 18 years old and \<66 years old) at the time of inclusion and eligible for an allogeneic stem cells transplantation and fit to receive the specified conditioning regimen * Patients with hematologic malignancies * Absence of a matched - related sibling donor (MSD) or a matched unrelated donor (MUD) 10/10 * Presence of two UCB units with the following criteria\*: HLA- matched 4/8, 5/8, 6/8, 7/8 or 8/8 for HLA- A, -B, -C and DRB1 loci AND • Presence of at least one UCB unit with the following criteria\*: ≥ 3 x 10e7 TNC/kg or ≥ 1.5 10e5 CD34+/kg pre- freezing \* For the UCB taken into HTLP culture, the CD34+ content does not need to meet the above cellularity criteria, as expansion during HTLP culture has been proven to ensure the appropriate number of CD7+ needed for each dose. The non- cultured UCB will be chosen to have a higher CD34+ cell content in order to enable long- term hematopoietic engraftment * Absence of Donor Specific Antibodies (DSA) with a MFI \> 5000 * Patient affiliated to social security * Written, informed consent of the patient Exclusion Criteria: * Any of the standard contraindications to allogeneic transplant * Left ventricular ejection fraction \<50% * Abnormal biochemistry results (ALT/AST\>10xULN, total bilirubin\>2.5xULN, creatinin clearance \<60ml/min) * Inability to understand and provide informed consent * Concomitant infectious disease: HTLV-I, HIV-I or HIV-II * Pregnancy or breastfeeding for women of childbearing potential * Patients with progressive hematologic malignancies * Previous participation within one month before inclusion in another protocol in which drugs may influence immune reconstitution of bone marrow transplantation