The projective Fraïssé limit of the family of all connected finite graphs with confluent epimorphisms

We investigate the projective Fraïssé family of finite connected graphs with confluent epimorphisms and the continuum obtained as the topological realization of its projective Fraïssé limit. This continuum was unknown before. We prove that it is indecomposable, but not hereditarily indecomposable, one-dimensional, Kelley, pointwise self-homeomorphic, but not homogeneous. It is hereditarily unicoherent and each point is the top of the Cantor fan. Moreover, the universal solenoid, the universal pseudo-solenoid, and the pseudo-arc may be embedded in it.