This study provides new arguments for the existence of local quasars, i.e. quasars in the vicinity of low redshift galaxies. Local quasars are probably ejected from respective parent galaxy. The sample includes 74 quasars in the vicinity of 8 different galaxies. Assuming for quasars the same distances from the observer, as for their respective parent galaxy, simple calculations lead to the quasars luminosities and radii. Furthermore, the assumption is made that the major part of redshifts of quasars are due to gravitational reddening, i.e. they are intrinsic in origin. In this way, data for masses and densities of quasars are obtained and a diagram Density-Redshift is constructed. Relationships are also found for: Absolute mag. - Radius, Absolute mag - Mass, Mass - Radius, and Mass - Luminosity for this sample of local quasars. Comparison with the same diagrams for stars suggests a possible connection between stars and quasars. All these relationships are compelling evidence that the assumptions and the procedure in this study are correct. The relationships found imply that local quasars behave like single bodies, or at least the bulk of the quasar s mass is a single body, close to its gravitational radius. The theory of such strange bodies does not yet exist. Local quasars show signs of evolution: their redshifts decrease with time, as their densities decrease. The physics behind this evolution is not yet clear. However, yet unknown physical processes might be involved, which cause the ejection of quasars by active galactic nuclei and the subsequent disintegration of matter of quasars. The end-product of this evolution (disintegration) could be small-mass companion galaxies. A relation “mass - density” is found, which could be explained if the speed of evolution (disintegration) depends on the mass of the quasar: more massive quasars evolve more rapidly.