  We consider a model of random walk in ${\mathbb Z}^2$ with (fixed or random)
orientation of the horizontal lines (layers) and with non constant iid
probability to stay on these lines. We prove the transience of the walk for any
fixed orientations under general hypotheses. This contrasts with the model of
Campanino and Petritis, in which probabilities to stay on these lines are all
equal. We also establish a result of convergence in distribution for this walk
with suitable normalizations under more precise assumptions. In particular, our
model proves to be, in many cases, even more superdiffusive than the random
walks introduced by Campanino and Petritis.
