  In this paper we prove that a classical theorem by McAdam about the analytic
spread of an ideal in a Noetherian local ring continues to be true for
divisorial filtrations on a two dimensional normal excellent local ring $R$,
and that the Hilbert polynomial of the fiber cone of a divisorial filtration on
$R$ has a Hilbert function which is the sum of a linear polynomial and a
bounded function. We prove these theorems by first studying asymptotic
properties of divisors on a resolution of singularities of the spectrum of $R$.
The filtration of the symbolic powers of an ideal is an example of a divisorial
filtration. Divisorial filtrations are often not Noetherian, giving a
significant difference in the classical case of filtrations of powers of ideals
and divisorial filtrations.
