Free, mixed and forced convection film boiling on a horizontal cylinder in a saturated or subcooled liquid is studied theoretically using a single model based on a two-phase laminar boundary layer integral method. The vapour flow is described accurately by including the inertia and convection terms in the momentum and energy equations, in order to study convection film boiling in the cases of very high superheat. Different film boiling cases are then analysed with this model. The case of high superheat and low subcooling was first analysed by comparing the model with an experiment consisting in the quenching of wires with very high superheat: the model was able to predict the measured heat transfer from the cylinder with errors less than 30%, performing better than previous models or correlations. Additional calculations in other high superheat conditions have also been performed and compared with a model which does not include the inertia and convection terms in order to have a more quantitative idea of their effects on the heat transfers. The case of low superheat and high subcooling is then analysed by comparing the model with other forced convection experiments with cylinders at lower temperatures. By analysing different experiments, it is found that there are in fact two different forced convection film boiling sub-regimes characterised by relatively ''low" or ''high" heat transfers, and that the existence of these sub-regimes is probably linked with the stability of the vapour film during film boiling. The model results compare quite well with the experimental data which belong to the ''stable" sub-regime but, on the other hand, the model largely underestimates the heat transfer for experimental data which belongs to the ''unstable" sub-regime. Finally, the model is compared to some free convection experimental data. The model was able to predict the measured heat transfers from the cylinder with errors less than 30% both in saturated and subcooled cases.