This trial aims to compare the safety of transplanting combinations of stem cells from placental with cord blood for a number of different malignant and benign haematological disorders. The trial is being conducted by the New York Medical College and will investigate whether giving placental stem cells at the same time as umbilical cord blood effects the survival of the transplanted stem. The trial expects to enrol 30 patients between March 2013 and December 2019 with any one of 16 diseases including several kinds of Leukaemia, Aplastic Anaemia as well as several benign but severely debilitating, incurable enzyme-linked metabolic disorders such as Gaucher's & Nieman-Pick disease. Patients will be monitored for complications and therapeutic benefit for nine months after the injection.