Nuclear star clusters (NSCs) are among the densest objects in the Universe. Despite their presence within the centres of an abundance of different galaxies, their origin and formation mechanisms remain shrouded in uncertainty. They are even found in the very smallest dwarf galaxies, down to stellar masses of just M_⋆ ∼ 5 × 10⁵ M_⊙. In this thesis, I aim to shed light on NSC formation in this low–mass regime by using cosmological simulations of isolated dwarfs.

I show that, at a spatial resolution of ∼3 pc, NSCs naturally emerge in dwarf galaxy simulations at a surprisingly low halo mass of just ∼ 5 × 10⁹ M_⊙. These form via a novel mechanism. If two galaxies near the mass threshold at which reionisation suppresses star formation undergo a major merger after reionisation, the compression of their substantial gas reservoirs can trigger a significant starburst. The NSC then forms from a mix of smooth and clumpy star formation in this starburst. The star clusters that form as a result of the clumpy star formation rapidly spiral to the centre to enhance the NSC. The starburst is sufficiently extreme that it shuts down any further star formation while transforming the

initially cusped central dark matter profile into a cored profile.

I discuss several implications of my new NSC–formation mechanism. Firstly, I show that it naturally leads to two stellar populations at the centre of the nucleated dwarf that have a large ∼billion–year age separation – one from the pre–reionisation star formation and the other from the NSC–forming starburst. This leads to a colour–magnitude diagram (CMD) that has two distinct main sequence turn–offs. Such strange CMDs have been observed in ∼11 Milky Way (MW) globular clusters (GCs), suggesting that they may be accreted NSCs. Secondly, I go on to show that if these MW GCs are accreted NSCs, then they will retain their central dark matter even when accounting for mass segregation. Furthermore, they are sufficiently dense and close that they become the most promising sites in the Universe to hunt for signatures of dark matter particle annihilation or decay. Finally, I combine my high–resolution dwarf galaxies simulations with a semi–empirical galaxy formation model to predict the number density of nucleated dwarfs below a stellar mass of M⋆ ∼ 10⁷ M_⊙ that should be found in the Local Universe. I show that this prediction gives a remarkably good match to the latest data from the MATLAS (Mass Assembly of early-Type GaLAxies with their fine Structures) survey, lending further support for my new model.