We consider the origins of enigmatic stellar populations in four Local Group galactic nuclei, specifically the Milky Way, M31, M32 and M33. These are centrally concentrated blue stars, found in three out of the four nuclear star clusters (NSCs) considered here. Their origins are unknown, but could include blue straggler (BS) stars, extended horizontal branch stars and young recently formed stars. Here, we calculate order-of-magnitude estimates for various collision rates, as a function of the host NSC environment and distance from the cluster centre. These rates are sufficiently high that BSs, formed via collisions between main sequence (MS) stars, could contribute non-negligibly ($sim$ 1-10% in mass) to every surface brightness profile, with the exception of the Milky Way. Stellar evolution models show that the envelopes of red giant branch (RGB) stars must be nearly completely stripped to significantly affect their photometric appearance, which requires multiple collisions. Hence, the collision rates for individual RGB stars are only sufficiently high in the inner $lesssim$ 0.1 pc of M31 and M32 for RGB destruction to occur. Collisions between white dwarfs and MS stars, which should ablate the stars, could offer a steady and significant supply of gas in every NSC in our sample. The gas could either fragment to form new stars, or accrete onto old MS stars already present. Thus, collisional processes could contribute significantly to the observed blue excesses in M31 and M33; future studies should be aimed at better constraining theoretical predictions to compliment existing and future observational data.
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