An extension of the BML model to the case of combustion of lean mixtures with variable equivalence ratio is presented in this paper. The dilution of both burnt products and fresh reactants by the surrounding air is taken into account by introducing the mixture fraction f in addition to the progress variable c. Statistical analysis of the reactive flow is achieved by using a joint pdf of c and f allowing calculation of mean quantities. Extinction of individual flamelets due to local dilution of fresh reactants is also considered. The influence of dilution, i.e., variable equivalence ratio, on the local mean heat release parameter as well as on the mean chemical production rate is described. Application of this modified model to the case of a stagnating turbulent flame stabilized close to a solid wall shows that the mean flame brush is predicted to be detached from the burner, in agreement with available experimental observations. Qualitative and quantitative modifications of the mean structure of the flame due to dilution are also investigated.