The wide spread of false information online including misinformation and disinformation has become a major problem for our highly digitised and globalised society. A lot of research has been done to better understand different aspects of false information online such as behaviours of different actors and patterns of spreading, and also on better detection and prevention of such information using technical and socio-technical means. One major approach to detect and debunk false information online is to use human fact-checkers, who can be helped by automated tools. Despite a lot of research done, we noticed a significant gap on the lack of conceptual models describing the complicated ecosystems of false information and fact checking. In this paper, we report the first graphical models of such ecosystems, focusing on false information online in multiple contexts, including traditional media outlets and user-generated content. The proposed models cover a wide range of entity types and relationships, and can be a new useful tool for researchers and practitioners to study false information online and the effects of fact checking.