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Relations for possible local quasars are studied: the “mass-radius”, “density-mass”, and “radius-density” relations. These relations show clear fragmentation and which is due to the presence of parallel sequences of observations. The cause for this unusual fragmentation is the presence of a term depending on rgr/rq in each respective relation. It seems therefore that fragmentation in these relations is due to evolution of quasars: as QSOs evolve, the ratio rgr/rq takes a sequence of discrete values and for each of these values there is a corresponding (different) relation. Each one of these three relations: “mass-radius”, “density-mass”, and “radius-density” evolve with the evolution of rgr/rq, building a “family” of relations. It is shown that the “mass-radius”, “density-mass”, and “radius-density” relations in their present versions hold also for stars, planets, and satellites, as well as for quasars. The linear density relation found previously for quasars and stars is now shown to apply also to the 9 planets and 19 satellites of the solar system. The existence of common relations, identical for quasars, stars, and planets leads to the conclusion that a link should probably exist between these structures. This link could be hidden in the origin of all these structures. The controversy with the gravitational collapse theory is obvious and needs further study.

Study of Possible Local Quasars IV. Effects of Discretization in Relations for QSOs and Search for Quasar-Stellar-Planetary Connections