The aim of this trial is to evaluate whether the prophylactic use of Defibrotide (DF) in pediatric patients (age less than 18 years) undergoing stem cell transplantation and who are at high risk of developing hepatic Veno-occlusive Disease (VOD) will have an impact on the incidence and severity of the disease. Patients will be randomly assigned to one of two treatment arms: Those allocated to the Prophylactic Arm will receive the study drug (Defibrotide) from the day of conditioning onwards. Patients allocated to the Control Arm will receive the study drug (Defibrotide) from the day that VOD is diagnosed.