MicroRNAs (miRNAs) are small non-coding RNAs which regulate gene expression by binding to the 3' UTR of the corresponding messenger RNAs. We construct miRNA co-target networks for a wide class of species (22 in total) using a target prediction database, MicroCosm Targets. For each species, miRNA pairs having one or more common target genes are connected and the number of co-targets are assigned as the weight of these links. We show that the link-weight distributions of all the species collapse remarkably onto each other when scaled suitably —the scale-factor turns out to be a measure of complexity of the species. A simple model, where targets are chosen randomly by miRNAs, could provide the correct scaling function and suggest that the increase of species complexity is related to the increase of the fraction of genes typically targeted by their miRNAs.