What is the maximum number of copies of a fixed forest in an -vertex graph in a graph class G as → ∞? We answer this question for a variety of sparse graph classes G. In particular, we show that the answer is Θ( ( ) ) where ( ) is the size of the largest stable set in the subforest of induced by the vertices of degree at most , for some integer that depends on G. For example, when G is the class of -degenerate graphs then = ; when G is the class of graphs containing no , -minor ( ) then = − 1;

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... nd when G is the class of -planar graphs then = 2. All these results are in fact consequences of a single lemma in terms of a finite set of excluded subgraphs. ( ) := ( [{ ∈ ( ) : deg ( ) }]).