  Let F be a global function field of characteristic p with ring of integers A
and let \Phi be a Hayes module on the Hilbert class field H(A) of F. We prove
an Iwasawa Main Conjecture for the Z_p^\infty-extension F/F generated by the
\mathfrak{p}-power torsion of \Phi (\mathfrak{p} a prime of A). The main tool
is a Stickelberger series whose specialization provides a generator for the
Fitting ideal of the class group of F. Moreover we prove that the same series,
evaluated at complex or p-adic characters, interpolates the Goss Zeta-function
or some p-adic L-function, thus providing the link between the algebraic
structure (class groups) and the analytic functions, which is the crucial part
of Iwasawa Main Conjecture.
