Laminar diffusion flames lifted on round jets are simulated using high order accurate numerical schemes. The results are examined in the light of analytical approximations of lift-off heights. A large variety of flame base topologies are observed when the fuel jet velocity is varied. Edge-flames, or triple-flames, progressively evolve into weakly varying partially premixed fronts, before blow-out occurs. The flame base is located on the stoichiometric surface at the point where the flow velocity is of the order of the stoichiometric and planar premixed flame burning velocity. In the simulations, this stabilization point is positioned further upstream than predicted by a frozen flow mixing description of the jet, even when effects of heat release and strain rate are included in the approximation of the triple-flame speed that is used to predict the lift-off height. The numerical results therefore suggest that the well known flow deflection, induced by heat release, brings the flame much closer to the burner than expected. Heat release is found to have a much stronger effect in the round jet than in the previously studied planar mixing layer. In the axisymmetric problem, this is attributed to the intricate coupling between the flow deflection and the position of iso-mixture fraction surfaces relatively to iso-velocity surfaces. Heat release also makes the flame base more robust than predicted by cold flow theory and helps to sustain large velocities before reaching the blow-out condition. Results suggest that the prediction of lift-off height cannot be reached without carefully accounting for the effect of heat release on the flow upstream of the flame base.