  We study the zero location and the asymptotic behavior of iterated integrals
of polynomials. Borwein-Chen-Dilcher's polynomials play an important role in
this issue. For these polynomials we find their strong asymptotics and give the
limit measure of their zero distribution. We apply these results to describe
the zero asymptotic distribution of iterated integrals of ultraspherical
polynomials with parameters $(2\alpha+1)/2$, $\alpha\in \mathbb{Z}_+$.
