We study the shape of the thick disc using photometric data at high and intermediate latitudes from SDSS and 2MASS surveys. We use the population synthesis approach using an ABC-MCMC method to characterize the thick disc shape, scale height, scale length, local density and flare, and we investigate the extend of the thick disc formation period by simulating several formation episodes. We find that the vertical variation in density is not exponential, but much closer to an hyperbolic secant squared. Assuming a single formation epoch, the thick disc is better fitted with a sech2 scale height of 470 pc and a scale length of 2.3 kpc. However if one simulates two successive formation episodes, mimicking an extended formation period, the older episode has a higher scale height and a larger scale length than the younger episode, indicating a contraction during the collapse phase. The scale height decreases from 800 pc to 340 pc, and the scale length from 3.2 kpc to 2 kpc. The star formation increases from the old episode to the young one. During the fitting process, the halo parameters are also determined. The constraint on the halo shows that a transition between a inner and outer halo, if exists, cannot be at a distance of less than about 30 kpc, which is the limit of our investigation using turnoff halo stars. Finally, we show that extrapolating the thick disc towards the bulge region explains well the stellar populations observed there, that there is no longer need to invoke a classical bulge. To explain these results, the most probable scenario for the thick disc is that it formed while the Galaxy was gravitationally collapsing from well mixed gas-rich giant clumps sustained by high turbulence which awhile prevent a thin disc to form, as proposed by Bournaud et al. (2009). This scenario explains the observations in the thick disc region as well as in the bulge region. (abridged)