Wharton Jelly Mesenchymal Stromal Cells as GVHD Prophylaxis

Inclusion Criteria: * With AML/ALL/SMD/SMP or lymphoid neoplasm requiring allogeneic stem cell transplantation * In complete response (CR) for AML/ALL or CR,partial response (PR) or non pre-treated for SMD/SMP and lymphoid neoplasm * Without a HLA matched related donor available and with identification of a haploidentical donor (brother, sister, parents, adult children or cousin) With usual criteria for HSCT: * ECOG ≤ 2 * No severe and uncontrolled infection * Cardiac function compatible with high dose of cyclophosphamide * Adequate organ function: ASAT and ALAT ≤ 2N, total bilirubin ≤ 1.5N, creatinine clearance ≥30ml/min (except if those abnormalities are linked to the hematological disease) * Requiring a RIC or non myeloablative conditioning: (i) \>50 years old; (ii) heavily pre-treated; (iii) Comoribidities according to Sorror et al. Blood 2005;106(8):2912-9, notamment HCT/CI≥ 3 (JAMA. 2011 Nov 2;306(17):1874-83). * With health insurance coverage (bénéficiaire ou ayant droit) * Understand informed consent or optimal treatment and follow-up * Contraception methods must be prescribed during all the duration of the research and using effective contraceptive methods during treatment and within 12 months for women of childbearing age and 6 months for men of childbearing age after the last dose of cyclophosphamide Exclusion Criteria: * History of Cancer in the last 5 years * Uncontrolled infection: Seropositivity for HIV or HTLV-1 or active hepatitis B or C defined by a positive PCR HBV or HCV and hepatic cytolysis due to HBV * Uncontrolled coronary insufficiency, recent myocardial infarction \<6 month, current manifestations of heart failure, uncontrolled cardiac rhythm disorders, ventricular ejection fraction \<50% * Pulmonary failure with DLCO\<50% * Addition of immunosuppressant treatment for GVHD prophylaxis (except immunosuppressant allowed per protocol) * Renal failure with creatinine clearance \<50ml / min * Pregnancy (β-HCG positive) or breast-feeding * Any debilitating medical or psychiatric illness which would preclude the realization of the SCT or the understanding of the protocol * Under protection by law (tutorship or curatorship) * Unwilling or unable to comply with the protocol