  We consider the classic infinite occupancy scheme, where balls are thrown in
boxes independently, with probability $p_j$ of hitting box $j$. Each time a box
receives its first ball we speak of a record and, more generally, call an
$r$-record every event when a box receives its $r$th ball. Assuming that the
sequence $(p_j)$ is not decaying too fast, we show that after many balls have
been thrown, the suitably scaled point process of $r$-record times is
approximately Poisson. The joint convergence of $r$-record processes is argued
under a condition of regular variation.
