  We study the global accretion-ejection solutions around a rotating black hole
considering three widely accepted pseudo-Kerr potentials that satisfactorily
mimic the space-time geometry of rotating black holes. We find that all the
pseudo potentials provide standing shock solutions for large range of flow
parameters. We identify the effective region of the shock parameter space
spanned by energy ($\mathcal{E}_{\text{in}}$) and angular momentum
($\lambda_{\text{in}}$) measured at the inner critical point ($x_{\text{in}}$)
and find that the possibility of shock formation becomes feeble when the
viscosity parameter ($\alpha$) is increased. In addition, we find that shock
parameter space also depends on the adiabatic index ($\gamma$) of the flow and
the shock formation continues to take place for a wide range of $\gamma$ as
$1.5 \le \gamma \le 4/3$. For all the pseudo potentials, we calculate the
critical viscosity parameter ($\alpha_{\text{shock}}^{\text{cri}}$) beyond
which standing shock ceases to exist and compare them as function of black hole
spin ($a_k$). We observe that all the pseudo potentials under consideration are
qualitatively similar as far as the standing shocks are concerned, however,
they differ both qualitatively and quantitatively from each other for rapidly
rotating black holes. Further, we compute the mass loss from the disc using all
three pseudo potentials and find that the maximum mass outflow rate ($R^{\rm
max}_{{\dot m}}$) weakly depends on the black hole spin. To validate our model,
we calculate the maximum jet kinetic power using the accretion-ejection
formalism and compare it with the radio jet power of low-hard state of the
black hole X-ray binaries (hereafter XRBs). The outcome of our results indicate
that XRBs along the `outliers' track might be rapidly rotating.
