  We analyse the location of extremely metal-poor stars (EMPs, [Fe/H]$ < -3$)
in 198 Milky Way (MW)/M31-like galaxies at $z=0$ in the TNG50 simulation. Each
system is divided into four kinematically-defined morphological stellar
components based on stellar circularity and galactocentric distance, namely
bulge, cold disk, warm disk, and stellar halo, in addition to satellites (with
stellar mass $\ge 5\times10^6\,M_\odot$). According to TNG50 and across all
simulated systems, the stellar halo of the main galaxy and satellites present
the highest frequency of EMPs (largest $M_{\mathrm{EMP,
comp}}$-to-$M_{\mathrm{tot, comp}}$ stellar mass ratio), and thus the highest
chances of finding them. Such frequency is larger in lower-mass than high-mass
satellites. Moreover, TNG50 predicts that the stellar halo of the main galaxy
always hosts and thus contributes the majority of the EMPs of the system.
Namely, it has the highest mass ratio of EMPs in it to all the EMPs in the
system (largest $M_{\mathrm{EMP, comp}}$-to-$M_\mathrm{EMP}
(<300\mathrm{kpc})$). However, notably, we also find that 33 MW/M31-like
galaxies in TNG50 have cold disks that contribute more than 10 per cent to the
total EMP mass, each with $\gtrsim 10^{6.5-7}\, M_\odot$ of EMPs in cold
circular orbits. These qualitative statements do not depend on the precise
definition of EMP stars, i.e. on the adopted metallicity threshold. The results
of this work provide a theoretical prediction for the location of EMP stars
from both a spatial and kinematic perspective and across an unprecedented
number of well-resolved MW/M31-like systems.
