How many FF’s are there in GG?

We prove that the asymptotic logarithmic density of copies of a graph FF in the graphs of a nowhere dense class CC is integral and we determine the range of its possible values. This leads to a generalization of the trichotomy theorem of Nešetřil and Ossona de Mendez (2011) [18] and to a notion of the degree of freedom of a graph FF in a class CC. This provides yet another formulation of the somewhere dense–nowhere dense classification. We obtain a structural result concerning the asymptotic shape of graphs with given degree of freedom.