  We examine the distributions of non-commutative polynomials of non-atomic,
freely independent random variables. In particular, we obtain an analogue of
the Strong Atiyah Conjecture for free groups thus proving that the measure of
each atom of any $n \times n$ matricial polynomial of non-atomic, freely
independent random variables is an integer multiple of $n^{-1}$. In addition,
we show that the Cauchy transform of the distribution of any matricial
polynomial of freely independent semicircular variables is algebraic and thus
the polynomial has a distribution that is real-analytic except at a finite
number of points.
