Patients will be assigned randomly to either the Defibrotide (DF) prophylaxis arm or the control arm. Those allocated to the DF prophylaxis arm (DF 25 mg/kg/d iv in 4 doses) will begin treatment at day of conditioning and stop at day +30 after Stem Cell Transplantation (SCT) or upon discharge from inpatient care. There is no dose adjustment for a patient of the study arm who developed VOD, they continue with the 25mg/kg/d iv.