  We investigate the star-formation rate (SFR) and stellar mass ($M_*$)
relation of a star-forming (SF) galaxy sample in the XMM-LSS field to $z\sim
3.0$ using the near-infrared data from the VISTA Deep Extragalactic
Observations (VIDEO) survey. Combining VIDEO with broad-band photometry, we use
the SED fitting algorithm CIGALE to derive SFRs and $M_*$ and have adapted it
to account for the full photometric redshift PDF uncertainty. Applying a SF
selection using the D4000 index, we find evidence for strong evolution in the
normalisation of the SFR-$M_*$ relation out to $z\sim 3$ and a roughly constant
slope of (SFR $\propto M_*^{\alpha}$) $\alpha=0.69\pm0.02$ to $z\sim 1.7$. We
find this increases close to unity toward $z\sim2.65$. Alternatively, if we
apply a colour selection, we find a distinct turnover in the SFR-$M_*$ relation
between $0.7\lesssim z\lesssim2.0$ at the high mass end, and suggest that this
is due to an increased contamination from passive galaxies. We find evolution
of the specific SFR $\propto(1+z)^{2.60}$ at $\log(M_*)\sim$10.5, out to
$z\lesssim2.4$ with an observed flattening beyond $z\sim$ 2 with increased
stellar mass. Comparing to a range of simulations we find the analytical
scaling relation approaches, that invoke an equilibrium model, a good fit to
our data, suggesting that a continual smooth accretion regulated by continual
outflows may be a key driver in the overall growth of SFGs.
