  The correlated and coupled dynamics of accretion and outflow around black
holes (BHs) are essentially governed by the fundamental laws of conservation as
outflow extracts matter, momentum and energy from the accretion region. Here we
analyzed a robust form of 2.5-dimensional viscous, resistive, advective
magnetized accretion-outflow coupling in BH systems, in the mean field
magnetohydrodynamical (MHD) regime. We solve the complete set of coupled MHD
conservation equations self-consistently, through invoking a generalized
polynomial expansion in two dimensions. We perform a critical analysis of
accretion-outflow region and provide a complete quasi-analytical family of
solutions for advective flows. We obtain the physical plausible outflow
solutions at high turbulent viscosity parameter $\alpha \, (\ge 0.3)$, and at a
reduced scale-height, as magnetic stresses compress or squeeze the flow region.
We found that the value of the large-scale poloidal magnetic field $\bar B_P$
is enhanced with increasing geometrical thickness of the accretion flow. On the
other hand differential magnetic torque ($-r^2 \bar B_{\varphi} \bar B_z$)
increases with the increase in $\dot M$. $\bar B_P$, $-r^2 \bar B_{\varphi}
\bar B_z$ as well as the plasma beta $\beta_P$ get strongly augmented with the
increase in the value of $\alpha$, enhancing the transport of vertical flux
outwards. Our solutions indicate that magnetocentrifugal acceleration plausibly
plays a dominant role in effusing out plasma from the radial accretion flow in
moderately advective paradigm which are more centrifugally dominated, however
in strongly advective paradigm it is likely that the thermal pressure gradient
would play a more contributory role in the vertical transport of the plasma.
