Limits of Baumslag-Solitar groups and dimension estimates in the space of marked groups

We prove that the limits of Baumslag-Solitar groups which we previously studied are non-linear hopfian C*-simple groups with infinitely many twisted conjugacy classes. We exhibit infinite presentations for these groups, classify them up to group isomorphism, describe their automorphisms and discuss the word and conjugacy problems. Finally, we prove that the set of these groups has non-zero Hausforff dimension in the space of marked groups on two generators.