Bartholdi's conjecture on finitely presented or densely related automaton groups

Let $G$ be a group generated by a finite state automaton. Bartholdi's conjecture. The group $G$ is either finitely presented or densely related. This conjecture concerns the relation range of groups generated by finite-state automata. The paper presents the Grigorchuk group as an example of a densely related group, but gives no resolution of the conjecture for all such groups.