The dynamics of ultrathin films of liquids with vanishing 3D volatility, on solid surfaces, has been modeled by assuming that the films can be taken to be adsorbed patches spreading under surface diffusion. When the phase behavior of the adsorbed films is taken into account, it is seen that a vapor patch will spread without limits and evolve into a Gaussian profile. For a liquid film which has low 2D volatility, a patch will appear to equilibrate and the surface ahead will remain dry. This is the "pancake," a case where a wetting liquid stops spreading. The spreading kinetics is generally seen to be the usual square-root-of-time type, although exceptions are also seen. A simple case of non-Fickian diffusion has been included, but fails to give anticipated results at least in a simple model.