The wetting phenomena on a compact spherical substrate of radius R, immersed in an one-component bulk vapor, are studied as functions of R and epsilon(W) (a parameter characterizing the adsorbent) within the context of Sullivan’s model. The substrate acts as an external potential V-ext(r) on fluid molecules; V-ext(r) is found by integrating over the adsorbent’s volume and its strength depends strongly on R. The fluid molecules are of constant diameter d. The density functional theory is used to analyze the structure of the wall-vapor interface by properly generalizing Sullivan’s model. For any value of R, the substrate is either incompletely wet or nonwet; the density profiles, labeled by epsilon(W), display only one growth mode, that from thin to thick film as epsilon(W) increases (in this case adsorption is always positive); for larger values of R, but small epsilon(W)’s, there is, in addition, another transition from nonwetting to wetting, adsorption now changes from negative to positive as epsilon(W) increases. In all cases, the thickness l of the wetting layer grown on the substrate is of the order of ln R. In conclusion, the effect of a spherical substrate on an one-component bulk vapor in comparison with that of a planar substrate is to reduce the three wetting classes of the planar adsorbent to two which are identified with class III, nonwetting, and class II, partial wetting with thin and thick films; class I, complete wetting, is absent.