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From what I've been able to gather, the very bright spot at the center of galaxies is produced by both the central quasar and a dense cluster of millions of stars that surround it. How much of the central light is produced by the quasar, and how much comes from the star cluster?

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Only a few percent of galaxies in the local universe have active galactic nuclei (e.g., Mishra & Dai 2020). The fraction with optically visible AGN (e.g., Seyfert nuclei) is lower than this, since in some galaxies only the X-ray or radio emission gets through the dust in the nuclear region of the galaxy. Even when the AGN is directly visible in optical light, it is usually significantly fainter than the rest of the galaxy. True quasars are quite rare.

So in most cases, the "very bright spot at the center" is produced by a dense accumulation of stars, either in a bulge of some kind or in a compact nuclear star cluster. This is the case for M101 (e.g., Kormendy et al. 2010), the galaxy whose image you presented in your question.

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Active Galactic Nuclei (AGNs) are very luminous galactic nuclei. In Quasars, a type of an AGN, the nucleus outshines the host galaxy. Therefore the main source of radiation is the nucleus, not the stars and the host.

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    $\begingroup$ While typically true, this answer would benefit from some numbers (with references) to back up the claim. $\endgroup$
    – pela
    Commented Dec 13, 2020 at 13:36
  • $\begingroup$ The majority of nearby galaxies do not have active nuclei. So for galaxies in general, the nuclear light is from stars. $\endgroup$
    – Peter Erwin
    Commented Dec 13, 2020 at 15:27
  • $\begingroup$ @PeterErwin I think the question is about galaxies that do show AGN activity though. $\endgroup$
    – pela
    Commented Dec 13, 2020 at 15:50
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    $\begingroup$ @pela I thought it was ambiguous, since it referred to "the bright spot at the center of galaxies", and seemed to imply that all galaxies had "a quasar", which is obviously not the case. $\endgroup$
    – Peter Erwin
    Commented Dec 15, 2020 at 19:10
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    $\begingroup$ The majority of AGN in the local universe do not outshine their host galaxies; some AGNs are quite faint, or only visible in X-rays, for example. $\endgroup$
    – Peter Erwin
    Commented Dec 15, 2020 at 19:12

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