  In this paper, we study the localization and propagation properties of the
edge states associated to a class of magnetic laplacians in $\mathbb{R}^2$. We
assume that the intensity of the magnetic field has a fast transition along a
regular and compact curve $\Gamma$. Our main results extend to a general
regular curve the study of the localised eigenfunction obtained when $\Gamma$
is a straight line (i.e. Iwatsuka models). Furthermore, we include in our
analysis the case of magnetic fields that slowly change along the curve
$\Gamma$ and we obtain a rigorous and explicit characterization of the
asymptotic mass distribution of the edge state along $\Gamma$.
