I will present an approach to simplicity of groupoid *-algebras associated to multispinal groups over Z_2 extending the method by Clark-Exel-Pardo-Starling-Sims in the case of the Grigorchuk group. As a key ingredient, we identify an infinite family of full-rank (0,1)-matrices of combinatorial flavour. The talk is based on joint work with Carla Farsi, Judith Packer and Nathaniel Thiem at UC Boulder, Colorado.
