  In this paper, we study the supports of measures in the free additive
convolution semigroup $\{\mu^{\boxplus t}:t>1\}$, where $\mu$ is a Borel
probability measure on $\mathbb{R}$. We give a formula for the density of the
absolutely continuous part of $\mu^{\boxplus t}$ and use this formula to obtain
certain regularizing properties of $\mu^{\boxplus t}$. We show that the number
$n(t)$ of the components in the support of $\mu^{\boxplus t}$ is a decreasing
function of $t$ and give equivalent conditions so that $n(t)=1$ for
sufficiently large $t$. Moreover, a measure $\mu$ so that $\mu^{\boxplus t}$
has infinitely many components in the support for all $t>1$ is given.
