Cover automata for finite languages have been much studied a few years ago.It turns out that a simple mathematical structure, namelysimilarity relations over a finite set of words, is underlying thesestudies. In the present work, we investigate in detail for themselvesthe properties of these relations beyond the scope of finite languages.New results with straightforward proofsare obtained in this generalized framework,and previous results concerning coverautomata are obtained as immediate consequences.