  In this paper we consider heavy tailed Markov renewal processes and we prove
that, suitably renormalised, they converge in law towards the $\ga$-stable
regenerative set. We then apply these results to the strip wetting model which
is a random walk $S$ constrained above a wall and rewarded or penalized when it
hits the strip $[0,\infty) \times [0,a]$ where $a$ is a given positive number.
The convergence result that we establish allows to characterize the scaling
limit of this process at criticality.
