  We develop and discuss a model formalism to study the properties of mass
outflows that are emerged out from a relativistic, magnetized, viscous,
advective accretion flow around a rotating black hole. In doing so, we consider
the toroidal component as the dominant magnetic fields and synchrotron process
is the dominant cooling mechanism inside the accretion disk. With this, we
self-consistently solve the coupled accretion-ejection governing equations in
the steady state and obtain the shock-induced global inflow-outflow solutions
in terms of the inflow parameters, namely plasma-$\beta$ ($=p_{\rm gas}/p_{\rm
mag}$, $p_{\rm gas}$ and $p_{\rm mag}$ being gas and magnetic pressures),
accretion rates ($\dot m$) and viscosity ($\alpha_{\rm B}$), respectively.
Using these solutions, we compute the mass outflow rate ($R_{\dot m}$, the
ratio of outflow to inflow mass flux) and find that mass loss from the
magnetized accretion disk continues to take place for wide range of inflow
parameters and black hole spin ($a_{\rm k}$). We also observe that $R_{\dot m}$
strongly depends on plasma-$\beta$, $\dot m$, $\alpha_{\rm B}$ and $a_{\rm k}$,
and it increases as the magnetic activity inside the accretion disk is
increased. Further, we compute the maximum mass outflow rate ($R^{\rm
max}_{\dot m}$) by freely varying the inflow parameters and find that for
magnetic pressure dominated disk, $R^{\rm max}_{\dot m} \sim 24\%$ ($\sim
30\%$) for $a_{\rm k}=0.0$ ($0.99$). Finally, while discussing the implication
of our model formalism, we compute the maximum jet kinetic power using $R^{\rm
max}_{\dot m}$ which appears to be in close agreement with the observed jet
kinetic power of several black hole sources.
