  We report the evolution of crystallographic structure, magnetic ordering and
electronic transport in thin films of full-Heusler alloy Co$_2$MnSi deposited
on (001) MgO with annealing temperatures ($T_A$). By increasing the $T_A$ from
300$^\circ$C to 600$^\circ$C, the film goes from a disordered nanocrystalline
phase to $B2$ ordered and finally to the $L2_1$ ordered alloy. The saturation
magnetic moment improves with structural ordering and approaches the
Slater-Pauling value of $\approx 5.0 \mu_B$ per formula unit for $T_A$ =
600$^\circ$C. At this stage the films are soft magnets with coercive and
saturation fields as low as $\approx$ 7 mT and 350 mT, respectively. Remarkable
effects of improved structural order are also seen in longitudinal resistivity
($\rho_{xx}$) and residual resistivity ratio. A model based upon electronic
transparency of grain boundaries illucidates the transition from a state of
negative $d\rho/dT$ to positive $d\rho/dT$ with improved structural order. The
Hall resistivity ($\rho_{xy}$) derives contribution from the normal scattering
of charge carriers in external magnetic field, the anomalous effect originating
from built-in magnetization and a small but distinct topological Hall effect in
the disordered phase. The carrier concentration ($n$) and mobility ($\mu$) have
been extracted from the high field $\rho_{xy}$ data. The highly ordered films
are characterized by $n$ and $\mu$ of 1.19$\times$ 10$^{29}$ m$^{-3}$ and 0.4
cm$^2V^{-1}s^{-1}$ at room temperature. The dependence of $\rho_{xy}$ on
$\rho_{xx}$ indicates the dominance of skew scattering in our films, which
shows a monotonic drop on raising the $T_A$. The topological Hall effect is
analyzed for the films annealed at 300$^\circ$C. ......
