  A polynomial family $\{p_n(x)\}$ is Appell if it is given by
$\frac{e^{xt}}{g(t)} = \sum_{n=0}^\infty p_n(x)t^n$ or, equivalently, $p_n'(x)
= p_{n-1}(x)$. If $g(t)$ is an entire function, $g(0)\neq 0$, with at least one
zero, the asymptotics of linearly scaled polynomials $\{p_n(nx)\}$ are
described by means of finitely zeros of $g$, including those of minimal
modulus. As a consequence, we determine the limiting behavior of their zeros as
well as their density. The techniques and results extend our earlier work on
Euler polynomials.
