The administration of high-dose chemotherapy followed by the infusion of blood or bone marrow stem cells (stem cell transplantation) from a matched donor has become standard treatment for patients with high-risk or relapsed hematological cancers. Currently, donors are found for approximately 80% of people who require such treatment, although the chance of finding a donor is much lower in some ethnic communities. In the current study the investigators will offer patients requiring transplantation, but for whom well matched donors cannot be identified either from within the family or on the donor registry, a transplant from a half-matched (haploidentical) family member. A myeloablative conditioning regimen and un-manipulated peripheral blood stem cells will be used. Post-transplant cyclophosphamide, tacrolimus and mycophenolate mofetil will be used to prevent graft versus host disease (GVHD). The primary outcome measure will be 6 month survival free from graft failure, relapse and grade 3-4 acute GVHD. Other outcomes of interest will include the frequency of Cytomegalovirus (CMV) or Epstein-Barr Virus (EBV) requiring treatment, overall survival and progression-free survival.