A univentricle with parallel pulmonary and systemic circulations is inherently inefficient because mixing of pulmonary and systemic venous return occurs. Thus a cavopulmonary anastomosis is used as a staged palliative procedure to reduce volume overload in patients with cyanotic congenital heart disease. On the basis of oxygen uptake and consumption, an equation was derived that related cardiac output, pulmonary venous oxygen saturation, upper body oxygen consumption, and superior-to-inferior vena caval blood flow ratio (QSVC/QIVC) to oxygen delivery. The primary findings were as follows. 1) As QSVC/QIVC increases, total body oxygen delivery and arterial and superior vena caval oxygen saturations increase. 2) As QSVC/QIVC increases, lower body oxygen delivery and inferior vena caval oxygen saturation initially increase, then peak, and then decrease. 3) As the percentage of lower body oxygen consumption increases, oxygen delivery and saturation decrease. 4) A cavopulmonary anastomosis decreases the required cardiac output for a given oxygen delivery. Thus we concluded that a high systemic arterial oxygen saturation after cavopulmonary anastomosis requires a high percentage of upper body oxygen consumption and a high QSVC/QIVC and that the cavopulmonary anastomosis reduces the volume load on the single ventricle.