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We continue the study of projective Fra\"iss\'e limits developed byIrwin-Solecki and Panagiotopoulos-Solecki by investigating families ofepimorphisms between finite trees and finite rooted trees. Ideas of monotone,confluent, and light mappings from continuum theory as well as severalproperties of continua are modified so as to apply them to topological graphs.As the topological realizations of the projective Fra\"iss\'e limits we obtainthe dendrite $D_3$, the Mohler-Nikiel universal dendroid, as well as new,interesting continua for which we do not yet have topologicalcharacterizations.

Projective Fra\"iss\'e limits of trees with confluent epimorphisms