  We study the short time properties of a two-dimensional film growth model in
which incident particles execute advective-diffusive motion with a vertical
step followed by $D$ horizontal steps. The model represents some features of
the deposition of anisotropic colloidal particles of the experiment in Phys.
Rev. Lett. {\bf 110}, 035501 (2013), in which wandering particles are attracted
to particle-rich regions in the deposit. Height profiles changing from rough to
columnar structure are observed as $D$ increases from $0$ (ballistic
deposition) to $8$, with striking similarity to the experimental ones. The
effective growth exponents matches the experimental estimates and the scaling
of those exponents on $D$ show a remarkable effect of the range of the
particle-deposit interaction. The nearly ellipsoidal shape of colloidal
particles is represented for the calculation of roughness exponents in
conditions that parallel the experimental ones, giving a range of estimates
that also include the experimental values. The effective dynamic exponents
calculated from the autocorrelation function are shown to be suitable to decide
between a true dynamic scaling or transient behavior, particularly because the
latter leads to deviations in an exponent relation. These results are
consistent with arguments on short time unstable (columnar) growth of Phys.
Rev. Lett {\bf 111}, 209601 (2013), indicating that critical quenched KPZ
dynamics does not explain that colloidal particle deposition problem.
