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MicroRNAs (miRNAs) are small RNA molecules, about 22 nucleotide long, which post-transcriptionally regulate their target messenger RNAs (mRNAs). They accomplish key roles in gene regulatory networks, ranging from signaling pathways to tissue morphogenesis, and their aberrant behavior is often associated with the development of various diseases. Recently it has been experimentally shown that the way miRNAs interact with their targets can be described in terms of a titration mechanism. From a theoretical point of view titration mechanisms are characterized by threshold effect at near-equimolarity of the different chemical species, hypersensitivity of the system around the threshold, and cross-talk among targets. The latter characteristic has been lately identified as competing endogenous RNA (ceRNA) effect to mark those indirect interactions among targets of a common pool of miRNAs they are in competition for. Here we propose a stochastic model to analyze the equilibrium and out-of-equilibrium properties of a network of [Formula: see text] miRNAs interacting with [Formula: see text] mRNA targets. In particular we are able to describe in detail the peculiar equilibrium and non-equilibrium phenomena that the system displays in proximity to the threshold: (i) maximal cross-talk and correlation between targets, (ii) robustness of ceRNA effect with respect to the model's parameters and in particular to the catalyticity of the miRNA-mRNA interaction, and (iii) anomalous response-time to external perturbations.