  Recent experiments on mesoscopic samples and theoretical considerations lead
us to analyze multiply charged ($n>1$) vortex solutions of the Ginzburg-Landau
equations for arbitrary values of the Landau-Ginzburg parameter $\kappa$. For
$n\gg 1$, they have a simple structure and a free energy ${\cal F}\sim n$.
  In order to relate this behaviour to the classic Abrikosov result ${\cal
F}\sim n^2$ when $\kappa\to +\infty$, we consider the limit where both $n\gg 1$
and $\kappa\gg1$, and obtain a scaling function of the variable $\kappa/n$ that
describes the cross-over between these two behaviours of ${\cal F}$. It is then
shown that a small-n expansion can also be performed and the first two terms of
this expansion are calculated. Finally, large and small n expansions are given
for recently computed phenomenological exponents characterizing the free energy
growth with $\kappa$ of a giant vortex.
