Three-dimensional (3D) micro/nano-structuring of photo-resists is systematically studied at the close-to-dielectric- breakdown irradiance. It is demonstrated that avalanche absorption is playing a major part in free electron generation and chemical bond breaking at these conditions. The steps of photo-initiation and chemical bond breaking in propagation of polymerization are altered as compared with photo-polymerization at low-irradiance and one-photon stereo-lithography. The avalanche dominates radical generation and promotion of polymerization at tight focusing and a high ∼TW/cm2 irradiance. The rates of electron generation by two-photon absorption and avalanche are calculated for the experimental conditions. Simulation results are corroborated by 3D polymerization in three resists with different photo-initiators at two different wavelengths and pulse durations. The smallest feature sizes of 3D polymerized logpile structures are consistent with spectral dependencies of the two photon nonlinearities. Implications of these findings for achieving sub-100 nm resolution in 3D structuring of photo-polymers are presented.