Atoms and regularity for measures in a partially defined free convolution semigroup

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The arithmetic of distributions in free probability theory (2005, methodology): “Note thatBercovici and Belinschi [8] gave a related approach using other analytic methods.”
Lectures on the Combinatorics of Free Probability (2006, background): “For analytic properties of the semigroup (μ )t≥1 see [5]; for a version for multiplicative free convolution see [6].”
On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution (2007, background): “The existence of μt was first observed in [17] in the case when μ has compact support, and then extended to arbitrary μ ∈ M in [4].”