  We give sufficient conditions for a subgroup of a tree almost automorphism
group to be isomorphic to the topological full groups of a one-sided shift in
the sense of Matui. As an application, we show that almost automorphism groups
of trees obtained from universal groups constructed by Burger and Mozes are
compactly generated and virtually simple. In addition, using the approach of
Bader, Caprace, Gelander and Mozes we show that some of these almost
automorphism groups do not have any lattice.
