  We apply the scale-length method to several three dimensional samples of the
Two degree Field Galaxy Redshift Survey. This method allows us to map in a
quantitative and powerful way large scale structures in the distribution of
galaxies controlling systematic effects. By determining the probability density
function of conditional fluctuations we show that large scale structures are
quite typical and correspond to large fluctuations in the galaxy density field.
We do not find a convergence to homogeneity up to the samples sizes, i.e. ~ 75
Mpc/h. We then measure, at scales r <~ 40 Mpc/h, a well defined and
statistically stable power-law behavior of the average number of galaxies in
spheres, with fractal dimension D=2.2 +- 0.2. We point out that standard models
of structure formation are unable to explain the existence of the large
fluctuations in the galaxy density field detected in these samples. This
conclusion is reached in two ways: by considering the scale, determined by the
linear perturbation analysis of a self-gravitating fluid, below which large
fluctuations are expected in standard models and through the determination of
statistical properties of mock galaxy catalogs generated from cosmological
N-body simulations of the Millenium consortitum.
