  The skew-normal and related families are flexible and asymmetric parametric
models suitable for modelling a diverse range of systems. We show that the
multivariate maximum of a high-dimensional extended skew-normal random sample
has asymptotically independent components and derive the speed of convergence
of the joint tail. To describe the possible dependence among the components of
the multivariate maximum, we show that under appropriate conditions an
approximate multivariate extreme-value distribution that leads to a rich
dependence structure can be derived.
