  Bouttier, Di Francesco and Guitter introduced a method for solving certain
classes of algebraic recurrence relations arising the context of embedded trees
and map enumeration. The aim of this note is to apply this method to three
problems. First, we discuss a general family of embedded binary trees, trying
to unify and summarize several enumeration results for binary tree families,
and also to add new results. Second, we discuss the family of embedded $d$-ary
trees, embedded in the plane in a natural way. Third, we show that several
enumeration problems concerning simple families of lattice paths can be solved
without using the kernel method by regarding simple families of lattice paths
as degenerated families of embedded trees.
