Flame stabilization and the mechanisms that govern the dynamics at the flame base have been subject to numerous studies in recent years. Recent results using a combined Large Eddy Simulation‐Conditional Moment Closure (LES‐CMC) approach to model the turbulent flow field and the turbulence‐chemistry interactions has been successful in predicting flame ignition and stabilization by auto‐ignition, but LES‐CMCs capability of the accurate modelling of the competition between turbulent quenching and laminar and turbulent flame propagation at the anchor point has not been resolved. This paper will consolidate LES‐CMC results by analysing a wide range of lifted flame geometries with different prevailing stabilization mechanisms. The simulations allow a clear distinction of the prevailing stabilization mechanisms for the different flames, LES‐CMC accurately predicts the competition between turbulence and chemistry during the auto‐ignition process, however, the dynamics of the extinction process and turbulent flame propagation are not well captured. The averaging process inherent in the CMC methods does not allow for an instant response of the transported conditionally averaged reactive species to the changes in the flow conditions and any response of the scalars will therefore be delayed. Stationary or quasi‐stationary conditions, however, can be well predicted for all flame configurations.