Univentricular heart is an uncommon congenital heart disease. A select group of these patients (those with severe pulmonary stenosis or atresia) can reach adult age with different degrees of heart failure and severe chronic hypoxemia. Patients with adequate pulmonary tree development are likely to undergo heart transplantation when usual palliative techniques are contraindicated. Three cases of univentricular heart with pulmonary stenosis in which heart transplantation was the optimal choice are reported. Different techniques used to assess pulmonary tree development are analysed.