This is a Phase IIb trial to determine if the delivery of the autologous UCB-MNC product into the myocardium of the right ventricle of the heart at the time of Stage II surgical repair will provide an improvement in cardiac function, reaching growth and developmental milestones, and quality of life, while also providing a reduction in the cumulative days of hospitalization following Stage II surgical repair. Long-term improvement in cardiac function, reaching growth and developmental milestones, reaching Stage III surgical repair pre-op work-up, prolonging time to cardiac transplantation or death, and improving quality of life will also be determined.