  Given a probability measure $\mu$ on the real line, there exists a semigroup
$\mu_t$ with real parameter $t>1$ which interpolates the discrete semigroup of
measures $\mu_n$ obtained by iterating its free convolution. It was shown in
\cite{[BB2004]} that it is impossible that $\mu_t$ has no mass in an interval
whose endpoints are atoms. We extend this result to semigroups related to
multiplicative free convolution. The proofs use subordination results.
