  Is it possible the no-hair paradigm is violated when a black hole undergoes
an instability? Employing massless charged scalar perturbations, we address
this question within the context of conformally invariant Einstein-Maxwell
theory for some allowed $d$-dimensional ($d=4n+4$ with conformal parameter
$n=0,1,2,...$ ) topological small AdS black-holes. We provide numerical
analyses that show the non trivial scalar hairy black hole solutions to include
planar and spherical horizon topologies in higher dimensions with an even
conformal parameter $n$. It is also shown that the solutions presented here
cannot be considered as scalar hairs for a Reissner-Nordstrom background. As a
result, for $d$-dimensional small AdS black holes in the presence of a
conformally invariant Maxwell source, the no-scalar hair paradigm seems to be
supported.
