Abstract
The concept of prolificity was previously introduced by the authors in the context of compositions of integers. We give a general interpretation of prolificity that applies across a range of relational structures defined in terms of counting embeddings. We then proceed to classify prolificity in permutation classes with bases consisting of permutations of length 2, or 3; completely classifying all such classes except Av(321). We then show a number of interesting properties that arise when studying prolificity in Av(321), concluding by showing that the class of permutations that are not prolific for any increasing permutation in Av(321) form a polynomial subclass.