  The hulls of linear and cyclic codes have been extensively studied due to
their wide applications.
  In this paper, the average dimension of the Hermitian hull of constacyclic
codes of length $n$ over a finite field $\mathbb{F}_{q^2}$ is determined
together with some upper and lower bounds. It turns out that either the average
dimension of the Hermitian hull of constacyclic codes of length $n$ over
$\mathbb{F}_{q^2}$ is zero or it grows the same rate as $n$. Comparison to the
average dimension of the Euclidean hull of cyclic codes is discussed as well.
