It seems natural to define the relation of "being a copy of" by means of the notion of similarity. While similarity is essential in the characterisation of the copying relation, a simple similarity account of such a relation does not seem to work. Counterexamples are easy to find. In this paper, we defend the idea that the copying relation should also be characterised by means of a dependence relation. It is not easy, however, to understand what kind of dependence relation is the right one. We will show that ontological and counterfactual forms of dependence are modally too strong and we, provisionally, try to use the modally weaker notion of historical dependence. Ontological, counterfactual and historical dependence share the common feature of being rigid notions of dependence. In the final section of the paper, we briefly discuss the idea that there might be non-rigid kinds of copying that therefore need to be characterised by means of non-rigid kinds of dependence.