Sovereignty in the digital space is a relatively new phenomenon, which is discussed in this paper. It is complex in nature and depends both on the technological base which is used (primarily network equipment, including 5G, etc.), software products and platforms, and on the promoted content. The countries are faced with the difficult task of regulating the activities of global media holdings in order to maintain value-based sovereignty. The author gives a political and economic analysis of value sovereignty, showing the importance of the state as a regulator that allows to eliminate negative informational externalities. Particular attention is paid to the analysis of the international media landscape and the formation of multipolarity in the network space, including the growing phenomenon of technological convergence in the media industry, as well as the positions of individual countries and regions in the global media industry. The corporate structures of the world’s largest media holdings are studied and the increasing degree of diversification of their assets is revealed. The generational differentiation of socialization mechanisms in the post-pandemic era, including the proportion of time devoted to social platforms, traditional media (the case of television), as well as the main ways of accessing the Internet and the penetration of new technologies. The most promising for socialization and fast-growing segments are shown, including Internet TV, virtual reality technologies, video games and cyber-sports. In the final part of the paper the author discusses the main problems and challenges of regulating the national media space in order to ensure value sovereignty in the era of global convergent media.