High-level Message Sequence Charts are a well-established formalism to specify scenarios of communications in telecommunication protocols. In order to deal with possibly unbounded specifications, we focus on star-connected HMSCs. We relate this subclass with recognizability and MSO-definability by means of a new connection with Mazurkiewicz traces. Our main result is that we can check effectively whether a star-connected HMSC is realizable by a finite system of communicating automata with possibly unbounded channels.