  Numerical simulations of black hole hot accretion flows have shown the
existence of strong wind. Those works focus only on the region close to black
hole thus it is unknown whether or where the wind production stops at large
radii. To address this question, Bu et al. (2016) have performed hydrodynamic
(HD) simulations by taking into account the gravitational potential of both the
black hole and the nuclear star clusters. The latter is assumed to be $\propto
\sigma^2 \ln(r)$, with $\sigma$ being the velocity dispersion of stars and $r$
be the distance from the center of the galaxy. It was found that when the
gravity is dominated by nuclear stars, i.e., outside of radius $R_A\equiv
GM_{\rm BH}/\sigma^2$, winds can no longer be produced. That work, however,
neglects the magnetic field, which is believed to play a crucial dynamical role
in the accretion and thus must be taken into account. In this paper, we revisit
this problem by performing magneto-hydrodynamical (MHD) simulations. We confirm
the result of Bu et al. (2016), namely wind can't be produced at the region of
$R>R_A$. Our result, combined with the results of Yuan et al. (2015), indicates
that the formula describing the mass flux of wind $\dot{M}_{\rm
wind}=\dot{M}_{\rm BH}(r/20r_s)$ can only be applied to the region where the
black hole potential is dominant. Here $\dot{M}_{\rm BH}$ is the mass accretion
rate at the black hole horizon and the value of $R_A$ is similar to the Bondi
radius.
