Context : A variety of formation scenarios have been proposed to explain the diversity of properties observed in bulges .
Studying their intrinsic shape can help to constraint the dominant mechanisms at the epochs of their assembly .

Aims : The structural parameters of a magnitude-limited sample of 148 unbarred S0–Sb galaxies were derived in order to study the correlations between bulges and disks , as well as the probability distribution function of the intrinsic equatorial ellipticity of bulges .

Methods : We present a new fitting algorithm ( GASP2D ) to perform two-dimensional photometric decomposition of the galaxy surface-brightness distribution .
This was assumed to be the sum of the contribution of a bulge and disk component characterized by elliptical and concentric isophotes with constant ( but possibly different ) ellipticity and position angles .
Bulge and disk parameters of the sample galaxies were derived from the J - band images , which were available in the Two Micron All Sky Survey .
The probability distribution function of the equatorial ellipticity of the bulges was derived from the distribution of the observed ellipticities of bulges and misalignments between bulges and disks .

Results : Strong correlations between the bulge and disk parameters were found .
About 80 \% of bulges in unbarred lenticular and early-to-intermediate spiral galaxies are not oblate but triaxial ellipsoids .
Their mean axial ratio in the equatorial plane is \langle B / A \rangle = 0.85 .
Their probability distribution function is not significantly dependent on morphology , light concentration or luminosity .
The possible presence of nuclear bars does not influence our results .

Conclusions : The interplay between bulge and disk parameters favors scenarios in which bulges have assembled from mergers and/or have grown over long times through disk secular evolution .
However , all these mechanisms have to be tested against the derived distribution of bulge intrinsic ellipticities .