  It is well known that if $h$ is a nonnegative harmonic function in the ball
of $\RR^{d+1}$ or if $h$ is harmonic in the ball with integrable boundary
values, then the radial limit of $h$ exists at almost every point of the
boundary. In this paper, we are interested in the exceptional set of points of
divergence and in the speed of divergence at these points. In particular, we
prove that for generic harmonic functions and for any $\beta\in [0,d]$, the
Hausdorff dimension of the set of points $\xi$ on the sphere such that
$h(r\xi)$ looks like $(1-r)^{-\beta}$ is equal to $d-\beta$.
