We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples .
These are the dilution effect and the small scale fluctuations .
We show that the various data that are considered as pointing to a homogenous distribution are all affected by these spurious effects and their interpretation should be completely changed .
In particular , we show that finite size effects strongly affect the determination of the galaxy number counts , namely the number versus magnitude relation ( N ( < m ) ) as computed from the origin .
When one computes N ( < m ) averaged over all the points of a redshift survey one observes an exponent \alpha = D / 5 \approx 0.4 compatible with the fractal dimension D \approx 2 derived from the full correlation analysis .
Instead the observation of an exponent \alpha \approx 0.6 at relatively small scales , where the distribution is certainly not homogeneous , is shown to be related to finite size effects .
We conclude therefore that the observed counts correspond to a fractal distribution with dimension D \approx 2 in the entire range 12 \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } \hss } \raise 2.0 pt% \hbox { $ \mathchar 316 $ } } m \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 5 % 36 $ } \hss } \raise 2.0 pt \hbox { $ \mathchar 316 $ } } 28 , that is to say the largest scales ever probed for luminous matter .
In addition our results permit to clarify various problems of the angular catalogs , and to show their compatibility with the fractal behavior .
We consider also the distribution of Radio-galaxies , Quasars and \gamma ray burst , and we show their compatibility with a fractal structure with D \approx 1.6 \div 1.8 .
Finally we have established a quantitative criterion that allows us to define and predict the statistical validity of a galaxy catalog ( angular or three dimensional ) .