  A univariate polynomial f over a field is decomposable if f = g o h = g(h)
for nonlinear polynomials g and h. In order to count the decomposables, one
wants to know, under a suitable normalization, the number of equal-degree
collisions of the form f = g o h = g^* o h^* with (g, h) = (g^*, h^*) and deg g
= deg g^*. Such collisions only occur in the wild case, where the field
characteristic p divides deg f. Reasonable bounds on the number of
decomposables over a finite field are known, but they are less sharp in the
wild case, in particular for degree p^2.
  We provide a classification of all polynomials of degree p^2 with a
collision. It yields the exact number of decomposable polynomials of degree p^2
over a finite field of characteristic p. We also present an efficient algorithm
that determines whether a given polynomial of degree p^2 has a collision or
not.
