  We investigate conditions for the existence of the limiting conditional
distribution of a bivariate random vector when one component becomes large. We
revisit the existing literature on the topic, and present some new sufficient
conditions. We concentrate on the case where the conditioning variable belongs
to the maximum domain of attraction of the Gumbel law, and we study geometric
conditions on the joint distribution of the vector. We show that these
conditions are of a local nature and imply asymptotic independence when both
variables belong to the domain of attraction of an extreme value distribution.
The new model we introduce can also be useful for simulations.
