The coordination of HVDC converters owned by different TSOs will raise the major question about operational responsibility of HVDC systems. The more complex HVDC system structures become and the more TSOs are involved in a single HVDC system the more important this question will become. This applies for meshed HVDC grids or even multiterminal HVDC systems owned by more than two TSOs. This paper proposes a transformation process for HVDC system operation starting with point-to-point HVDC links owned by two different TSOs up to multi-TSO operated HVDC grids. This transformation process can be seen as a starting point of a development to establish a single HVDC grid controller capable of operating at a global optimum. This concept paper also discusses analogies between AC and DC systems regarding stability and security categories.