  We study the probability distribution of residence time of a grain at a site,
and its total residence time inside a pile, in different ricepile models. The
tails of these distributions are dominated by the grains that get deeply buried
in the pile. We show that, for a pile of size $L$, the probabilities that the
residence time at a site or the total residence time is greater than $t$, both
decay as $1/t(\ln t)^x$ for $L^{\omega} \ll t \ll \exp(L^{\gamma})$ where
$\gamma$ is an exponent $ \ge 1$, and values of $x$ and $\omega$ in the two
cases are different. In the Oslo ricepile model we find that the probability
that the residence time $T_i$ at a site $i$ being greater than or equal to $t$,
is a non-monotonic function of $L$ for a fixed $t$ and does not obey simple
scaling. For model in $d$ dimensions, we show that the probability of minimum
slope configuration in the steady state, for large $L$, varies as $\exp(-\kappa
L^{d+2})$ where $\kappa$ is a constant, and hence $ \gamma = d+2$.
