Background: The Fontan procedure is the last of three stages of congenital heart surgery to treat children born with a single ventricle heart defect. In these patients, a balanced hepatic blood flow distribution (HFD) towards both lungs is important, since a lack of “hepatic factor” has been associated with the formation of pulmonary arteriovenous malformations (PAVMs). With imaging modalities and computational fluid dynamics (CFD), the hepatic blood flow distribution can be studied. Recent CFD studies indirectly quantify HFD to both lungs by tracking ‘hepatic flow’ particles that are uniformly seeded in the Fontan tunnel and analyzing the distribution of these particles towards both lungs (conventional approach). However, this approach is based on the unvalidated assumption that there is a uniform distribution of hepatic blood flow in the Fontan tunnel. Aside from CFD modeling, previous clinical imaging studies showed that respiration has a tremendous impact on the hepatic blood flow in Fontan patients; however, these studies only used Doppler Ultrasound because the resolution of real-time phase-contrast magnetic imaging resonance (PC-MRI) is not yet good enough for direct hepatic flow quantification. Objectives: this study aimed to investigate the distribution of hepatic blood flow in the Fontan tunnel using CFD simulations. Another objective was to quantify the HFD towards both lungs using particle tracking directly from the inlets of the hepatic veins (novel approach) and compare these HFD results to the conventional approach. Furthermore, we performed an in-depth flow analysis and developed a new method to indirectly quantify the hepatic flow in the hepatic veins and the respiratory effects on it using real-time PC-MRI. Methods: Unsteady CFD modeling was used to assess the mixing of hepatic blood flow within the Fontan tunnel and the different HFD quantification methods. Therefore, we created three-dimensional reconstructions of the patient-derived Fontan anatomies based on MRI imaging that included the geometry of the hepatic veins in the computational fluid domain. We created two types of CFD models: 1. CFD models that only included the cardiac effects on blood flow, and 2. CFD models that considered both the cardiac and respiratory effects on blood flow. For the in-depth flow analysis using real-time PC-MRI, we first measured the blood flow in the Fontan tunnel, just above the entrance of the hepatic veins. Second, we derived the IVC blood flow below the hepatic veins. By subtracting these flows, we indirectly quantified the hepatic blood flow. Results and conclusion: The main findings were that hepatic blood flow was non-uniformly distributed within the Fontan tunnel and substantial differences in HFD between the conventional approach and novel approach were found in both types of CFD models that either ignored or considered respiration. Additionally, we showed that it was feasible to indirectly measure hepatic blood flow in Fontan patients while using real-time PC-MRI. These derived flow parameters extracted from real-time PC-MRI acquisitions confirmed what previously has been described that the hepatic blood flow in Fontan patients was heavily influenced by respiration.