Monte Carlo simulations have been carried out to study argon adsorption on graphite at temperatures below the bulk triple point temperature, Ttr(bulk) = 83.8 K. Two models for graphite have been used to investigate the effects of an adsorbate patch with a free boundary on the layering temperatures, the two-dimensional (2D)-triple point and the 2D-critical point for the three adsorbate layers on the surface. The first model (S-model) has a planar surface of infinite extent in the two directions parallel to the surface, and the second is a finite (2D-patch model). Although simulations using both models describe the characteristic temperatures, only the 2D-patch model can represent the experimental isotherms accurately, and the condensation pressures at which first-order transitions occur, while simulations with the S-model yield many unphysical substeps that are not observed experimentally in the first layer adsorbate, which leads to a poor description of higher adsorbate layers. These results support the interpretation that boundary growth of an adsorbate patch is the mechanism for argon adsorption at temperatures below the bulk triple point temperature. Combining the results derived from this simulation study for temperatures below the bulk triple point temperature, with results reported in the literature for temperatures above Ttr(bulk) and experimental data, we have constructed a generic pattern for the adsorption isotherms of simple gases on graphite at temperatures ranging from well below the bulk triple point temperature up to the bulk critical temperature, a comprehensive description not widely recognized in the literature.