A Q star was, according to the Fifth Doctor, "very rare". When one burned out, it created quad magnetism. A Q star was known to exist in the area of space known to the TARDIS information system as Rondel, or, more anciently, the Arc of Infinity. (TV: Arc of Infinity)
Polyphilos was a Q star. Rassilon and Omega destroyed the star in order to create the Eye of Harmony. (PROSE: The Scrolls of Rassilon)