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From a macro perspective, a single network system normally shows second-order phase transitions, but for a coupled network method, it shows rich percolation behaviors for several coupling strength, coupling patterns and coupling mechanisms. Although the giant component accounts for a huge proportion in the genuine system, it can not be neglected that when the network scale is big sufficient, the scale of finite-size connected elements has an important influence on network connectivity. We right here systematically analyze the phase transition behaviors of finite-size connected components that are diverse from the giant element from a meso-microscopic point of view. Studying percolation...