  We consider an anisotropic version of Baxter's model of `sticky hard
spheres', where a nonuniform adhesion is implemented by adding, to an isotropic
surface attraction, an appropriate `dipolar sticky' correction (positive or
negative, depending on the mutual orientation of the molecules). The resulting
nonuniform adhesion varies continuously, in such a way that in each molecule
one hemisphere is `stickier' than the other. We derive a complete analytic
solution by extending a formalism [M.S. Wertheim, J. Chem. Phys. \textbf{55},
4281 (1971) ] devised for dipolar hard spheres. Unlike Wertheim's solution
which refers to the `mean spherical approximation', we employ a
\textit{Percus-Yevick closure with orientational linearization}, which is
expected to be more reliable. We obtain analytic expressions for the
orientation-dependent pair correlation function $g(1,2) $. Only one equation
for a parameter $K$ has to be solved numerically. We also provide very accurate
expressions which reproduce $K$ as well as some parameters, $\Lambda_{1}$ and
$\Lambda_{2}$, of the required Baxter factor correlation functions with a
relative error smaller than 1%. We give a physical interpretation of the
effects of the anisotropic adhesion on the $g(1,2) $. The model could be useful
for understanding structural ordering in complex fluids within a unified
picture.
