  The growth of confined magnetic films with ferromagnetic interactions between
nearest-neighbor spins is studied in a stripped $(1+1)-$dimensional rectangular
geometry. Magnetic films are grown irreversibly by adding spins at the
boundaries of the growing interface. A competing situation with two opposite
short range surface magnetic fields of the same magnitude is analyzed. Due to
the antisymmetric condition considered, an interface between domains with spins
having opposite orientations develops along the growing direction. Such
interface undergoes a localization-delocalization transition that is identified
as a quasi-wetting transition, in qualitative agreement with observations
performed under equilibrium conditions. In addition, the film also exhibits a
growing interface that undergoes morphological transitions in the growth mode.
It is shown that, as a consequence of the nonequilibrium nature of the
investigated model, the subtle interplay between finite-size effects, wetting,
and interface growth mechanisms leads to more rich and complex physical
features than in the equilibrium counterpart. Indeed, a phase diagram that
exhibits eight distinct regions is evaluated and discussed. In the
thermodynamic limit, the whole ordered phase (which contains the quasi-wetting
transition) collapses, while within the disordered phase, standard
extrapolation procedures show that only two regions are present in the phase
diagram of the infinite system.
