It has recently been suggested that the competition for a finite pool of microRNAs (miRNA) gives rise to effective interactions among their common targets (competing endogenous RNAs or ceRNAs) that could prove to be crucial for post-transcriptional regulation (PTR). I shall discuss a minimal model of PTR where the emergence and the nature of such interactions can be characterized in detail at steady state. Sensitivity analysis shows that binding free energies and repression mechanisms are the key ingredients for the cross-talk between ceRNAs to arise. Interactions emerge in specific ranges of repression values, can be symmetrical (one ceRNA influences another and vice-versa) or asymmetrical (one ceRNA influences another but not the reverse) and may be highly selective, while possibly limited by noise. However, I will also show that non-trivial correlations among ceRNAs can emerge in experimental readouts even in absence of miRNA-mediated cross-talk simply due to transcriptional fluctuations.