tokens: we find the following results: The central regions of the simulated MW mass-sized galaxies are found to be populated mainly by stars older than 10 Gyr in three of the analysed haloes (Aq-B has ∼50 per cent of its stars >10 Gyr). Most of these stars formed in situ, with a fraction of old stars in the range ∼0.10–0.35 contributed by satellite accretion. The spatial distributions of in situ and accreted stars are different – accreted stars form centrally concentrated spheroidal distributions, while the in situ components exhibit clear bar structures or elongated distributions. The predicted kinematics are consistent with these properties. In particular, the rotational velocity and velocity dispersion distributions of the central region of Aq-C resemble those reported by Zoccali et al. ( 2017 ). Both in situ and accreted stars in the central regions formed in main starbursts (in the progenitor and accreted satellites, respectively). However, accreted stars formed early, so that there is mean age difference of ∼0.5–1 Gyr between the in situ and accreted stars. The age distributions of in situ stars exhibit a tail towards younger ages. Aq-B has a more uniform star formation history for both in situ and accreted stars, since it is affected by a more recent merger event. The age distributions are consistent with the central regions being dominated by stars older than 10 Gyr. This finding is in agreement with the observational results of Santucci et al. ( 2015 ) and Carollo et al. ( 2016 ), who identified an ACS in the MW, extending out to beyond the Sun's location. The metallicity distributions of the in situ and accreted stars are slightly different. The metallicity distributions of the accreted stars are shifted towards lower abundances than those of the in situ stars, and the former have higher α-element enhancements. These trends are consistent with their formation history, since the accreted stars are formed in satellite galaxies with dynamical masses smaller than 10 10 M ⊙ (Tissera et al. 2014 ), while the in situ stars formed in the main progenitors. Regarding the old stars, they represent most of the stars in the central regions, on average. In our simulations, old, accreted stars belong preferentially to the stellar haloes within the inner 10 kpc. A mass fraction of ∼35 per cent is part of the bulge components. The accretion histories show that Aq-A and Aq-C received larger contributions from smaller satellites. On the other hand, the central regions of Aq-B and A-D experienced a greater contribution from a few massive accreted dwarf galaxies. As a consequence, the former have more metal-poor and α-element enhanced stellar populations. At a fiducial solar radius, we estimate that ∼40 per cent of the old stars are accreted. This fraction is in reasonable agreement with the recent results of An et al. ( 2015 ) for the solar neighbourhood. All the analysed central regions have a small fraction of stars younger than 0.1 Gyr, ∼3 per cent, on
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