  We consider the generalised PageRank walk on a digraph $G$, with refresh
probability $\alpha$ and resampling distribution $\lambda$. We analyse
convergence to stationarity when $G$ is a large sparse random digraph with
given degree sequences, in the limit of vanishing $\alpha$. We identify three
scenarios: when $\alpha$ is much smaller than the inverse of the mixing time of
$G$ the relaxation to equilibrium is dominated by the simple random walk and
displays a cutoff behaviour; when $\alpha$ is much larger than the inverse of
the mixing time of $G$ on the contrary one has pure exponential decay with rate
$\alpha$; when $\alpha$ is comparable to the inverse of the mixing time of $G$
there is a mixed behaviour interpolating between cutoff and exponential decay.
This trichotomy is shown to hold uniformly in the starting point and uniformly
in the resampling distribution $\lambda$.
