  In this paper we consider Wronskian polynomials labeled by partitions that
can be factorized via the combinatorial concepts of $p$-cores and
$p$-quotients. We obtain the asymptotic behavior for these polynomials when the
$p$-quotient is fixed while the size of the $p$-core grows to infinity. For
this purpose, we associate the $p$-core with its characteristic vector and let
all entries of this vector simultaneously tend to infinity. This result
generalizes the Wronskian Hermite setting which is recovered when $p=2$.
