  An exhaustive numerical investigation of the growth of magnetic films in
confined $(d+1)$-dimensional stripped geometries ($d=1,2$) is carried out by
means of extensive Monte Carlo simulations. Thin films in contact with a
thermal bath are grown by adding spins with two possible orientations and
considering ferromagnetic (nearest-neighbor) interactions. At low temperatures,
it is observed that the films exhibit ``spontaneous magnetization reversals''
during the growth process. Furthermore, it is found that for $d=1$ the system
is non-critical, while a continuous order-disorder phase transition at finite
temperature takes place in the $d=2$ case. Using standard finite-size scaling
procedures, the critical temperature and some relevant critical exponents are
determined. Finally, the growth of magnetic films in $(2+1)$ dimensions with
competing short-range magnetic fields acting along the confinement walls is
studied. Due to the antisymmetric condition considered, an interface between
domains with spins having opposite orientation develops along the growing
direction. Such an interface undergoes a localization-delocalization transition
that is the precursor of a wetting transition in the thermodynamic limit.
Furthermore, the growing interface also undergoes morphological transitions in
the growth mode. A comparison between the well-studied equilibrium Ising model
and the studied irreversible magnetic growth model is performed throughout.
Although valuable analogies are encountered, it is found that the
nonequilibrium nature of the latter introduces new and rich physical features
of interest.
