To investigate the effect of pulsatility of venous flow waveform in the inferior and superior caval vessels on the performance of functional and "failing" Fontan patients based on two primary performance measures - the conduit power loss and the distribution of inferior caval flow (hepatic factors) to the lungs. Doppler angiography flows were acquired from two typical extra-cardiac conduit "failing" Fontan patients, aged 13 and 25 years, with ventricle dysfunction. Using computational fluid dynamics, haemodynamic efficiencies of "failing", functional, and in vitro-generated mechanically assisted venous flow waveforms were evaluated inside an idealised total cavopulmonary connection with a caval offset. To investigate the effect of venous pulsatility alone, cardiac output was normalised to 3 litres per minute in all cases. To quantify the pulsatile behaviour of venous flows, two new performance indices were suggested. Variations in the pulsatile content of venous waveforms altered the conduit efficiency notably. High-frequency and low-amplitude oscillations lowered the pulsatile component of the power losses in "failing" Fontan flow waveforms. Owing to the offset geometry, hepatic flow distribution depended strongly on the ratio of time-dependent caval flows and the pulsatility content rather than mixing at the junction. "Failing" Fontan flow waveforms exhibited less balanced hepatic flow distribution to lungs. The haemodynamic efficiency of single-ventricle circulation depends strongly on the pulsatility of venous flow waveforms. The proposed performance indices can be calculated easily in the clinical setting in efforts to better quantify the energy efficiency of Fontan venous waveforms in pulsatile settings.