Inclusion Criteria:  Diagnosis of a congenital hear defect with functionally single right ventricle (such as HLHS, HLHS variants, unbalanced AV septal defect with R dominance, DORV with Hypoplastic LV) undergoing Fontan surgical palliation At least 2 and less than or equal to 5 years of age at time of Fontan surgical palliation For subjects enrolling in the treatment arm, previous participation in clinical trial Umbilical Cord Blood Collection and Processing for Hypoplastic Left Heart Syndrome patients (NCT01856049) with autologous UCB-MNC product collected and available for distribution is required.  Exclusion Criteria:  History of DMSO reaction (treatment arm only subjects). Parent(s) or legal guardian unwilling to have their child participate or unwilling to follow the study procedures. Severe chronic diseases at the discretion of the treating physician. Extensive extra-cardiac syndromic features. History of cancer.  Any of the following complications of his/her congenital heart disease:  any condition requiring urgent, or unplanned intervention procedure within 15 days prior to Fontan surgical palliation, unless complete and full cardiac recovery is documented by site investigator. severe pulmonary hypertension (reported in the medical record as >70% systemic pressure) Other clinical concerns as documented by a site investigator that would predict (more likely to happen than not to happen) a risk of severe complications or very poor outcome, not directly related tot he stem cell product or its injection procedure, during or after Fontan surgical palliation. Individuals with severe heart failure that requires heart transplantation Individuals with refractory or worsening arrhythmia Individuals with an automated implantable cardioverter defibrillator (AICD) or pacemaker Patient with prior surgical complications during the Fontan surgical palliation that resulted in or could be reasonably expected to significantly decrease cardiac function