Open capillary flows are increasingly used in biotechnology, biology, thermics, and space science. So far, the dynamics of capillary flows has been studied mostly for confined channels. However, the theory of open microfluidics has considerably progressed during the last years, and an expression for the travel distance has been derived, generalizing the well-known theory of Lucas, Washburn, and Rideal. This generalization is based on the use of the average friction length and generalized Cassie angle. In this work, we successively study the spontaneous capillary flow in uniform cross section open rounded Ugrooves-for which methods to determine the friction lengths are proposed-the flow behavior at a bifurcation, and finally flow in a simple-loop network. We show that after a bifurcation, the Lucas-Washburn-Rideal law needs to be adapted and the relation between the travel distance and time is more complicated than the square root of time dependency.