This work is a formal linguistic study of the analogous polygenetic emergence and optional omissibility of a syncretic that-type complementiser across the Germanic (Part I), Romance (Part II), ¿Balkan¿ (Part III) and Celtic (Part IV) branches of the Indo-European family. It has, however, many parts which seem redundant but actually aim at providing a solid background about the Indo-European language family being treated in each section, as well as some very interesting appendixes. Cover image: Confronted leopards above a banqueting scene in the Tomb of the Leopards, Etruscan Necropolis of Monterozzi (480¿450 BC).