  The dynamics of black hole seeds in high redshift galaxies is key to
understand their ability to grow via accretion and to pair in close binaries
during galactic mergers. To properly follow the dynamics of black holes we
develop a physically motivated model to capture unresolved dynamical friction
from stars, dark matter and gas. We first validate the model and then we use it
to investigate the dynamics of seed black holes born at $z\sim9$ in dwarf
proto-galaxies. We perform a suite of zoom cosmological simulations with
spatial resolution as high as 10 pc and with a stellar and dark matter mass
resolution of $2\times10^3 \, \textrm{M}_\odot$ and $2\times10^5 \,
\textrm{M}_\odot$ respectively. We first explore the dynamics of a seed black
hole in the galaxy where it is born and show that it is highly erratic if the
seed mass is less than $10^5\, \textrm{M}_\odot$. The dynamics is dominated by
the stellar component, whose distribution is irregular and patchy, thus
inducing stochasticity in the orbits: the black hole may be anywhere in the
proto-galaxy. When this dwarf merges into a larger galaxy, it is paramount to
simulate the process with very high spatial and mass resolution in order to
correctly account for the stripping of the stellar envelope of the satellite
black hole. The outcome of the encounter could be either a tight binary or, at
least temporary, a wandering black hole, leading to multiple black holes in a
galaxy, each inherited from a different merger.
