  In this paper we investigate some properties of Rees algebras of divisorial
filtrations and their analytic spread. A classical theorem of McAdam shows that
the analytic spread of an ideal $I$ in a formally equidimensional local ring is
equal to the dimension of the ring if and only if the maximal ideal is an
associated prime of $R/\overline{I^n}$ for some $n$. We show in Theorem 1.6
that McAdam's theorem holds for $\mathbb Q$-divisorial filtrations in an
equidimensional local ring which is essentially of finite type over a field.
This generalizes an earlier result for $\mathbb Q$-divisorial filtrations in an
equicharacteristic zero excellent local domain by the author. This theorem does
not hold for more general filtrations.
  We consider the question of the asymptotic behavior of the function $n\mapsto
\lambda_R(R/I_n)$ for a $\mathbb Q$-divisorial filtration $\mathcal I=\{I_n\}$
of $m_R$-primary ideals on a $d$-dimensional normal excellent local ring. It is
known from earlier work of the author that the multiplicity $$ e(\mathcal I)=d!
\lim_{n\rightarrow\infty}\frac{\lambda_R(R/I_n)}{n^d} $$ can be irrational. We
show in Lemma 4.1 that the limsup of the first difference function $$
\limsup_{n\rightarrow\infty}\frac{\lambda_R(I_n/I_{n+1})}{n^{d-1}} $$ is always
finite for a $\mathbb Q$-divisorial filtration. We then give an example in
Section 4 showing that this limsup may not exist as a limit.
  In the final section, we give an example of a symbolic filtration
$\{P^{(n)}\}$ of a prime ideal $P$ in a normal two dimensional excellent local
ring which has the property that the set of Rees valuations of all the symbolic
powers $P^{(n)}$ of $P$ is infinite.
