  Let $\mu$ denote a Borel probability measure and let $\{ \mu_{t} \}_{t\geq
1}$ denote the free additive convolution semigroup of Nica and Speicher. We
show that the support of these measures varies continuously in the Hausdorff
metric for $t >1$. We utilize complex analytic methods and, in particular, a
characterization of the absolutely continuous portion of these supports due to
Huang.
