  We revisit an unpublished paper of Vervoort (2002) on the once reinforced
random walk, and prove that this process is recurrent on any graph of the form
$\mathbb{Z}\times \Gamma$, with $\Gamma$ a finite graph, for sufficiently large
reinforcement parameter. We also obtain a shape theorem for the set of visited
sites, and show that the fluctuations around this shape are of polynomial
order. The proof involves sharp general estimates on the time spent on
subgraphs of the ambiant graph which might be of independent interest.
