  The growth of magnetic films with ferromagnetic interactions between
nearest-neighbor spins is studied in $(d+1)-$dimensional rectangular geometries
for $d = 1,2$. Magnetic films are grown irreversibly by adding spins at the
boundaries of the growing interface. The orientation of the added spins depends
on both the energetic interaction with already deposited spins and the
temperature, through a Boltzmann factor. At low temperatures thin films, of
thickness $L$, are constituted by a sequence of well ordered magnetic domains.
Spins belonging to each domain, of average length $l_{D} \gg L$, have mostly
the same orientation, but consecutive domains have opposite magnetization. Such
kind of ``spontaneous magnetization reversal'' during the growth process has a
short characteristic length $l_{R}$, such that $l_{D} \gg l_{R} \sim L$. At
higher temperatures, a transition between ordered and disordered states is also
observed. The emerging behavior is compared to that of the equilibrium Ising
model.
