  In this paper we prove generic results concerning Hardy spaces in one or
several complex variables. More precisely, we show that the generic function in
certain Hardy type spaces is totally unbounded and hence non-extentable,
despite the fact that these functions have non tangential limits at the
boundary of the domain. We also consider local Hardy spaces and show that
generically these functions do not belong, not even locally, to Hardy spaces of
higher order. We work first in the case of the unit ball of Cn where the
calculations are easier and the results are somehow better, and then we extend
them to the case of strictly pseudoconvex domains.
