The Fontan repair is a three-stage palliative surgical procedure for single ventricle congenital heart diseases, ultimately resulting in the right heart bypass. This is accomplished by routing the systemic venous return directly to the lungs. Although this procedure reduces the mortality rate, its long-term outcome is still considered far from optimal. Over the years several modifications have been suggested, ultimately leading to the total cavopulmonary connection (TCPC), which is the current procedure of choice. A better understanding of the hemodynamics in the TCPC is critical for further optimization of the TCPC design and surgical planning, which may lead to improved surgical outcome. Recent experimental and numerical studies have focused on characterizing the fluid dynamics of the TCPC but to date no study has attempted to relate the geometry of the TCPC anatomies with their hemodynamic parameters. The present study therefore proposes to quantify the complex geometrical characteristics of patient-specific TCPC anatomies and correlate these characteristics with their hemodynamic efficiency. A technique using skeletonization approach is thus developed to achieve this goal. The centerline approximation of the TCPC geometry is used to extract main geometric parameters such as vessel area, curvature and offset. The developed methodology is then applied to characterize the shape of various TCPC templates including extra-cardiac (EC) and intra-atrial (IA) TCPCs, TCPCs with bilateral Superior Vena Cavae and geometries before the third stage. The obtained geometric parameters are then related to the TCPC hemodynamics, particularly to the power loss.