Could habitable worlds exist around a quasi-star?

Size comparison of the hypothetical quasi star to the solar system.

We don’t think that rocky planets could form around the largest stars in the universe, the quasi-stars.

The largest known normal star, Stephenson 2–18, is more than 2000 times larger in diameter than the Sun, but quasi-stars were even more than 10 to 100 times as big still. For many years they had been largely only hypothetical, but since we powered the James Webb Space Telescope in 2021, it spotted strange red dots in the early universe, and there is now speculation that some might be quasi-stars. If it proves to be true, then it would confirm their existence when the universe was very young.

Normal stars like the Sun shine because of ongoing nuclear fusion. Quasi-stars shone because they were so massive that a black hole formed inside them and ate them from within. This feasting never lasted long; at most 7 to 10 million years, and this is how long quasi-stars lived.

They could have only existed just after the Big Bang and were some of the first stars that formed. After the primordial gas was polluted by first dying regular stars that exploded as supernovae, quasi-stars couldn’t form anymore. They can’t coalesce from gas enriched too much by heavier atomic nuclei.

Therefore, at the time, there was no material to form rocky planets. There was some lithium, but it was too dilute, and there was no dust it could accumulate onto to form bigger grains and pebbles, which could form rocky planets.

Furthermore, the beastly quasi-stars produced hyperwinds. Gas around them couldn’t have cooled enough to settle into gas giant planets. It wouldn’t settle into them also because there was no dust, pebbles, and rock around which gas could accumulate anyway. Maybe very rarely, gas cloud fragmentation could have occurred, producing brown dwarf stars more than 13 times the mass of Jupiter, but brown dwarfs are nowhere near being habitable worlds.

What is meant by superhabitable planet?

 A superhabitable planet is a hypothetical type of exoplanet that could be more suitable than Earth for the origin and evolution of life.

Here's what such a planet would look like:

With oceans that are shallower than Earth's and narrower continents, which means fewer to no deserts.

Green up to the poles suggests a warmer atmosphere which, since the ideal mass for a superhabitable planet would be about 1.2 Earth gravities, would not be caused by greenhouse gases, but only from a denser atmosphere.

The atmosphere should be rich in oxygen, but not much more than Earth has; too much oxygen and fires would become more frequent.

What is not shown in these two pics is a moon, which some consider essential for the development of life due to tides, which "stir" materials along the coasts, and because it is believed that a moon is necessary for a stable axial tilt.