Inclusion Criteria:  Availability of suitably matched unrelated donor (9/10 or 10/10)  Planned to receive one of the following RIC protocols:  Fludarabine-Melphalan (Fludarabine 120-180mg/m2 IV; melphalan ≤ 150mg/m2 IV) BEAM or LEAM (carmustine 300mg/m2 IV or lomustine 200mg/m2 IV with: etoposide 800 mg/m2 IV; cytarabine 1600mg/m2 IV; melphalan 140mg/m2 IV) Fludarabine-Busulphan (Fludarabine 120-180mg/m2 IV; Busulphan ≤ 8mg/kg PO or 6.4mg/kg IV) Planned use of PBSCs for transplantation  Planned allo-SCT for one of the following haematological malignancies:  AML in CR (patients enrolled onto the COSI trial are not eligible for this study) ALL in CR (patients enrolled onto the ALL-RIC trial are not eligible for this study) CMML <10% blasts MDS <10% blasts (patients enrolled onto the COSI trial are not eligible for this study) NHL in CR/PR HL in CR/PR MM in CR/PR CLL in CR/PR CML in 1st or 2nd chronic phase Myelofibrosis Age 16-70 years Females of and male patients of reproductive potential (i.e., not post-menopausal or surgically sterilised) must agree to use appropriate, highly effective, contraception from the point of commencing therapy until 12 months after transplant  Exclusion Criteria:  Use of any method of graft manipulation (excluding storage of future DLI) Use of alemtuzumab or any method of T cell depletion except those that are protocol-defined Known hypersensitivity to study drugs or history of hypersensitivity to rabbits Pregnant or lactating women Adults of reproductive potential not willing to use appropriate, highly effective, contraception during the specified period Life expectancy <8 weeks Active HBV or HCV infection  Organ dysfunction defined as:  LVEF <45% GFR <50ml/min Bilirubin >50µmol/l AST/ALT>3 x ULN Participation in COSI or ALL-RIC trials Contraindication to treatment with the study drugs (Thymoglobulin, cyclophosphamide, sirolimus, ciclosporin and mycophenolate mofetil) as detailed in each study drug SPC. Patient has any other systemic dysfunction (e.g., gastrointestinal, renal, respiratory, cardiovascular) or significant disorder which, in the opinion of the investigator would jeopardise the safety of the patient by taking part in the trial.