The dynamics of a system of three long Josephson transmission lines co
upled at a common end point is investigated. We report several periodi
c fluxon states and trace out the corresponding zero field steps. The
boundary conditions at the common point lead to a very different stabi
lity of steps for odd and even numbers of fluxons. In addition we find
two ''normal state'' branches for the IV curve, where either two or t
hree of the branches are in their normal state.