We present a modified version of our "sliding model", where chain arcs, between two contacts at the surface, may move if all the barriers along the arc are weaker than a certain threshold.An important advance of the revised model is that the high limiting chain lengths N* observed in the experiments are naturally accoundted for. In this model, a film of thickness h, smaller than the coil size, can show either a "sandwich" structure with two mobile sublayers (at low temperatures T<T(h)), or a single mobile layer at T>T(h). But the accident occurring at T=T(h), does not necessarily coincide with the apparent glass transition, determined by the intersection of two tangents in a plot of thickness versus temperature.