  We prove that, for every $0 \leq t \leq 1$, the limiting distribution of the
scale-normalized number of key comparisons used by the celebrated algorithm
QuickQuant to find the $t$th quantile in a randomly ordered list has a
Lipschitz continuous density function $f_t$ that is bounded above by $10$.
Furthermore, this density $f_t(x)$ is positive for every $x > \min\{t, 1 - t\}$
and, uniformly in $t$, enjoys superexponential decay in the right tail. We also
prove that the survival function $1 - F_t(x) =
\int_x^{\infty}\!f_t(y)\,\mathrm{d}y$ and the density function $f_t(x)$ both
have the right tail asymptotics $\exp [-x \ln x - x \ln \ln x + O(x)]$. We use
the right-tail asymptotics to bound large deviations for the scale-normalized
number of key comparisons used by QuickQuant.
