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Nuclear star clusters (NSCs) are massive star clusters found in the innermostregion of the majority of galaxies. While recent studies suggest that low-massNSCs in dwarf galaxies form largely out of the merger of globular clusters andNSCs in massive galaxies have assembled most of their mass through central starformation, the formation channel of the Milky Way's NSC is still uncertain. Inthis work, we use GigaEris, a very high resolution $N$-body hydrodynamicalcosmological ``zoom-in'' simulation, to investigate NSC formation in theprogenitor of a Milky Way-sized galaxy, as well as its relation to the assemblyand evolution of the galactic nuclear region. We study the possibility thatbound, young, gas-rich, stellar clusters within a radius of 1.5~kpc of the maingalaxy's centre at $z>4$ are the NSC predecessors (NSCPs). We identify 53systems which satisfy our criteria, with a total baryonic mass of$10^{7.7}$~M$_{\odot}$. They have a relatively low mean stellar metallicity($-0.47 \lesssim {\rm [Fe/H]} \lesssim -0.11$) in comparison to the present-daystars in the Milky Way's NSC. The NSCPs with a `born thin-disc' star fraction,$F_{\rm thin}$, higher than 0.5 are older and display slightly differentproperties than the clusters with $F_{\rm thin} \leq 0.5$. We demonstrate thatboth stellar cluster accretion and in-situ star formation will contribute tothe formation of the NSC, providing evidence for an hybrid formation scenariofor the first time in an $N$-body, hydrodynamical, cosmological ``zoom-in''simulation. Furthermore, we also identify a nuclear stellar ring in thesimulation, with properties similar to those of the Milky Way's nuclear stellardisc.

Stellar cluster formation in a Milky Way-sized galaxy at z>4 -- II. A  hybrid formation scenario for the nuclear star cluster and its connection to  the nuclear stellar ring