  The goal of this article is to prove that every surface with a regular point
in the three-dimensional projective space of degree at least four, is of wild
representation type under the condition that either $X$ is integral or
$\mathrm{Pic}(X) \cong \langle \Oo_X(1) \rangle$; we construct families of
arbitrarily large dimension of indecomposable pairwise non-isomorphic aCM
vector bundles. On the other hand, we prove that every non-integral aCM scheme
of arbitrary dimension at least two, is also very wild in a sense that there
exist arbitrarily large dimensional families of pairwise non-isomorphic aCM
non-locally free sheaves of rank one.
