  We study holomorphic functions attaining weighted norms and its connections
with the classical theory of norm attaining holomorphic functions. We prove
that there are polynomials on $\ell_p$ which attain their weighted but not
their supremum norm and viceversa. Nevertheless, we also prove that in the
context of polynomials of fixed degree both norms are in fact equivalent. This
leads us to the main problem of the paper, namely, whether the holomorphic
functions attaining their weighted norm are dense. Although we exhibit an
example where this does not hold, as the main theorem of our paper, we prove
the denseness provided the domain space is uniformly convex. In fact, we
provide a Bollob\'as type theorem in this setting. For the proof of such a
result we develop a new geometric technique.
