New evidence of quasi-two-dimensional (2D) behaviour in granular bulk high-T c samples is presented. Anomalously large differences between the mean-field critical temperature and the temperature of the Berezinsky-Kosterlitz-Thouless-like transition is found to be in good agreement with calculations based on the small inherent thickness of CuO 2 layers. Two successive mechanisms, quasiparticle and Josephson tunnelling, are used to explain the experimental data obtained on a large set of samples ranging from one unit cell to perfect single crystals. A simple phenomenological analysis based on the renormalization of 2D superfluid density of charge carriers through the thickness-restrictive mechanism of their mean free path is developed.