One cord blood unit may replace two in stem cell transplants for blood cancer

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Age ≥ 18 and \< 66 years * Patient with acute myeloid leukemia (AML) high risk in 1st complete remission: * CR1 obtained by 2 cycles of chemotherapy, * unfavorable Cytogenetics * FLT3 Duplication, * Or acute myeloid leukemia (AML) in 2nd complete remission, * Or acute lymphoblastic leukemia (ALL) High-risk 1st complete remission: * Presence of the translocation t (9; 22), * Or acute lymphoblastic leukemia (ALL) in 2nd complete remission, * Or Chronic Myeloid Leukemia (LCM) beyond the 1st chronic phase * Or Myelodysplasia or with IPSS score with 2 or more * Or Hodgkin's disease in sensitive relapse or beyond the 2nd complete remission. or following types of lymphoma : * Diffuse large B lymphoma cells relapsed or refractory after two lines of treatment or after a line with autologous hematopoietic stem cell, or * Mantle cell lymphoma relapsed or refractory after two lines of treatment or after a line with autologous hematopoietic stem cell * Others aggressive lymphoma for which an indication of allograft is selected (Burkitt lymphoma, lymphoblastic lymphoma, intravascular lymphoma, ...) * Lymphoma (low-grade follicular lymphoma, marginal zone lymphoma) in histological transformation. * Low-grade lymphoma for which an indication of allograft is retained * Unable to receive myeloablative conditioning because of age (\> 45 years) and/or the existence of co-morbidities precluding a myeloablative conditioning (status ECOG \> / = 2, DLCO \<50%, fungal infection proven or probable in the previous 60 days) and / or prior treatment with total body irradiation at doses above 2 Gy or busulfan doses\> 8 mg/kg * No contra-indication for a transplant in allogeneic non-myeloablative conditioning, * No HLA-identical sibling, * Absence of an unrelated donor on national or international registering with a 10/10 allelic matching or a 9/10 allelic matching with the only tolerated mismatches being: HLA-C. * No unit of placental blood available fulfilling the characteristics of compatibility (HLA compatible at least 4/6 allele or generic) and richness * Provision of at least 2 units of placental blood, whose compatibility is 4/6, 5/6 or 6/6 and whose richness is before thawing, \> 2 x 107 and \< 3 to 4 x 107 nucleated cells per/kg. * Patient affiliated to a social security scheme, * Free and informed consent signed by the patient and the investigator. Exclusion Criteria: * Age \<18 and ≥ 66 years * Malignant myeloid or lymphoid acute or chronic disease without indication for an allogeneic transplant according to the criteria of European Bone Marrow Transplantation Group. * Able to receive a myeloablative conditioning because of age (\<45 years) and the absence of co morbidities (status ECOG\> / = 2, DLCO \<50%, fungal infection proven or probable in 60 preceding days) and the absence of prior treatment with total body irradiation at doses above 2 Gy or busulfan doses\> 8 mg / kg * Contra indication for a non-myeloablative conditioning, * HLA-identical sibling available * Availability of an unrelated donor on a national or international register with 10/10 or 9/10 HLA matching (HLA-C Mismatch tolerated). * At least one unit of cord blood available with the characteristics of compatibility (HLA compatible at least 4/6 allelic or generic) and richness (before thawing\> / = 3 to 4 x 107 nucleated cells/kg recipient, by degree of compatibility) * Absence of at least 2 units of placental blood, whose compatibility is 4/6, 5/6 / or 6/6 and whose richness before thawing is \> 2 x 107 and \< 4 x 107 nucleated cells per/kg of recipient. * Women of childbearing age not using contraception, pregnant or lactating