  We address the estimation of quantiles from heavy-tailed distributions when
functional covariate information is available and in the case where the order
of the quantile converges to one as the sample size increases. Such "extreme"
quantiles can be located in the range of the data or near and even beyond the
boundary of the sample, depending on the convergence rate of their order to
one. Nonparametric estimators of these functional extreme quantiles are
introduced, their asymptotic distributions are established and their finite
sample behavior is investigated.
