  The aim of this work is to provide the first examples of $n$-dimensional
varieties of wild representation type, for arbitrary $n\geq 2$. More precisely,
we prove that all Fano blow-ups of $\PP^n$ at a finite number of points are of
wild representation type exhibiting families of dimension of order $r^2$ of
simple (hence, indecomposable) ACM rank $r$ vector bundles for any $r\geq n$.
In the two dimensional case, the vector bundles that we construct are moreover
Ulrich bundles and $\mu$-stable with respect to certain ample divisor.
