  The correct detection of the Berezinskii-Kosterlitz-Thouless (BKT) transition
in quasi-two-dimensional superconductors still remains a controversial issue.
Its main signatures, indeed, are often at odds with the theoretical
expectations. In a recent work\cite{me} we have shown that the presence of
spatially correlated disorder plays a key role in this sense being it the
reason underlying the experimentally-observed smearing of the universal
superfluid-density jump. In the present paper, we closely investigate the
effects of correlated disorder on the BKT transition, addressing specifically
the issue whether it changes or not the BKT universality class.
