  We investigate the properties of mergers comparable to the
Gaia-Sausage-Enceladus (GSE) using cosmological hydrodynamical simulations of
Milky Way-like galaxies. The merger progenitors span an order of magnitude in
their peak stellar mass ($3\times10^8<M_{\star}/\rm{M}_{\odot}<4\times10^9$)
and include both rotation and pressure-supported galaxies ($0.10<D/T<0.77$). In
a minority of cases, the GSE-like debris is comprised of stars from more than
one merger progenitor. However, there is a close similarity in their
chemodynamical properties and the triaxial shapes of their debris, and so it is
not always possible to distinguish them. The merger progenitors host a variety
of luminous satellites ($0-8$ with $M_{\star}>10^6\,\rm{M}_{\odot}$), but most
of these do not follow the merger to low orbital energies. Between $0-1$ of
these satellites may survive to $z=0$, but with no clear signatures of their
past association. We show that the fraction of stars originating from GSE-like
mergers is reduced for lower metallicities (reaching a minimum around
$\text{[Fe/H]} = -2$), and also within $5\,$kpc of the galactic centre. Whilst
these central regions are dominated by in-situ stars, the ex-situ fraction
trends towards a 100 per cent asymptote when considering the most metal-poor
stars ($\text{[Fe/H]}\ll-2.5$). Considering this, its near proximity, and its
small volume on the sky, the Galactic centre lends itself as a prime
environment in the search for the stars from the earliest galaxies, whilst
avoiding contamination from GSE stars.
