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Bright squeezed vacuum (BSV) is a macroscopic non-classical state of light with huge photon numbers per mode, high degree of entanglement and noise reduction below the standard quantum limit. These reasons give rise to the wide range of applications of BSV, for example, in quantum imaging, metrology, quantum optomechanics, etc. An integral part of BSV generation is the spatial walk-off effect that limits the efficiency of nonlinear optical interactions. This effect plays as usual destructive role in experiment however it is possible to overcome such negative influence. In contrast to the low-gain PDC, to develop fully consistent theoretical description of the strongly pumped (high-gain) BSV seems to be a rather difficult problem due to the contribution of correlated high-order Fock components and non-applicability of the perturbation theory. In our work we present fully analytical description of the angular spectrum and correlations of BSV, and explain the anisotropy effects and the effect of spatial walk-off from the point of view of the Schmidt modes. We show that by only tilting of the crystal it is possible to obtain giant twin-beam generation that can be used in different applications. The obtained theoretical results are compared with the experimental data in high-gain regime and are found to be in a good agreement. The physics of the found effects is explained in terms of collective Schmidt modes of the system.