  JWST has detected many overmassive galactic systems at $z > 4$, where the
mass of the black hole, $M_\bullet$, is $10-100$ times larger than expected
from local relations, given the host's stellar mass, $M_\star$. This Letter
presents a model to describe these overmassive systems in the high-$z$
Universe. We suggest that the black hole mass is the main driver of high-$z$
star formation quenching. SMBHs globally impact their high-$z$ galaxies because
their hosts are physically small, and the black holes have duty cycles close to
unity at $z > 4$. In this regime, we assume that black hole mass growth is
regulated by the quasar's output, while stellar mass growth is quenched by it
and uncorrelated to the global properties of the host halo. We find that the
ratio $M_\bullet/M_\star$ controls the average star formation efficiency: if
$M_\bullet/M_\star > 8\times 10^{18} (n \Lambda/f_{edd})[(\Omega_b
M_h)/(\Omega_m M_\star) - 1]$, then the galaxy is unable to form stars
efficiently. Once this ratio exceeds the threshold, a runaway process brings
the originally overmassive system towards the local $M_\bullet - M_\star$
relation. Furthermore, the $M_\bullet - M_\star$ relation evolves with redshift
as $\propto (1+z)^{5/2}$. At $z \sim 5$, we find an overmassive factor of $\sim
55$, in excellent agreement with current JWST data and the high-$z$ relation
inferred from those. Extending the black hole horizon farther in redshift and
lower in mass will test this model and improve our understanding of the early
co-evolution of black holes and galaxies.
