Context. The history of our Galaxy is shaped by significant merger events, which contribute to its mass and to the distribution of stars, but which also bring globular clusters that act as the main tracers of the accretion history of the Milky Way. Aims. We investigated Gaia-Enceladus/Sausage globular cluster samples and studied their orbital and dynamical evolution over cosmological timescales in external time-variable potential. We estimated the limits of distribution of the escaped stars from the globular clusters’ orbital evolution in energy angular momentum space. Methods. To reconstruct the orbital evolution of the known globular clusters of the dwarf galaxy Gaia-Enceladus/Sausage, we used the parallel N-body code φ-GPU. We investigated the relationship between globular clusters and their progenitor by analysing their orbital parameters and phase-space distribution during 9 Gyr of evolution in the past. We created a N-body model of Gaia-Enceladus/Sausage globular clusters and analysed their dynamical evolution and distribution of the escaped stars today. Results. We summarised the samples of the Gaia-Enceladus/Sausage globular clusters and created two main categories: ‘most probable’ and ‘tentative’, with 15 and 9 clusters, respectively. We analysed the evolution of their kinematic, orbital, and phase-space parameters in the external time-variable potential. We defined phase-space distribution limits of stars that escape from globular clusters during 9 Gyr of evolution: a specific energy from −18 to −12.2 ×10⁴ km² s⁻², Lz from −0.98 to 0.72 ×10³ kpc km s⁻¹, and Lperp from 0 to 1.8 ×10³ kpc km s⁻¹. The limits of the GE/S debris in Galactic area based on orbital parameters of the GC’s escaped stars are: for apocentre and pericetre distances of 10–28 and 1–4 kpc, <18 kpc in Galactocentric radius and <|15| kpc in the Z direction. Generally we compared the phase-space distribution of escaped stars from the GCs GE/S debris energy-angular momentum limits with the observed very metal-poor stars, which belong to the GE/S itself and produce consistent results.

Context. To date, two main mechanisms have been proposed for the formation and growth of nuclear star clusters (NSCs) in galaxies. The first suggests in situ star formation from gas that has migrated to the central regions from the galaxy’s outskirts, while the second involves the accretion of stars from disrupted globular clusters (GCs) onto the galactic centre. However, the relative importance of these mechanisms in the evolution of NSCs across different galaxy morphologies remains an open question. Aims. We investigate the accretion of GC stars on early cosmological timescales through detailed N-body simulations of theoretical GC models to assess the role of this mechanism in Milky Way-like (MW-like) galaxies. Methods. For the dynamical modelling, we used the updated parallel N-body code ϕ-GPU, including stellar evolution. We prepared three sets of GC models with different half-mass radii (rhm), each consisting of 50 full N-body GC models, and integrated these models in an external, time-variable MW-like potential taken from the cosmological database IllustrisTNG-100. The simulations cover the time interval from −10 Gyr to −5 Gyr, enabling us to assess the rate of early stellar accretion onto the proto-NSC. Results. We find that GC models with average orbital eccentricities of 0.4−0.5 and orbits oriented perpendicular to the galactic disc contribute most significantly to the mass of the proto-NSC formation. Accretion is especially efficient in the first billion years (Gyr) and in compact GC models with rhm=1 pc. In all sets, the dominant accreted stellar population consists of low-mass stars (≈ 0.33 M⊙). However, the accreted mass alone is insufficient to fully account for the current NSC mass. Conclusions. Based on our extended set of numerical simulations, we obtained an average lower limit of mass contribution (≈ 6%) to the NSC from investigated GCs. The fraction of mass contribution from individual disrupted GCs can significantly vary from 0.1% up to 90%. Generally, we conclude that the GC stellar accretion channel alone might not be sufficient to ensure the present-day MW galaxy’s NSC mass budget.