  We study the class of groups generated by automata that act essentially
freely on the boundary of a rooted tree. In the process we establish and
discuss some general tools for determining if a group belongs to this class,
and explore the connections of this class to the classes of just-infinite and
scale-invariant groups. Our main application is a complete classification of
groups generated by 3-state automata over 2-letter alphabet that are in this
class.
