Bamfordviruses are arguably the most diverse group of viruses infecting eukaryotes. They include the Nucleocytoplasmic Large DNA viruses (NCLDVs), virophages, adenoviruses,Mavericksand Polinton-like viruses. Two main hypotheses for their origins have been proposed: the ‘nuclear-escape’ and ‘virophage-first’ hypotheses. The nuclear-escape hypothesis proposes an endogenous,Maverick-like ancestor which escaped from the nucleus and gave rise to adenoviruses and NCLDVs. In contrast, the virophage-first hypothesis proposes that NCLDVs coevolved with protovirophages;Mavericksthen evolved from virophages that became endogenous, with adenoviruses escaping from the nucleus at a later stage. Here, we test the predictions made by both models and consider alternative evolutionary scenarios. We use a data set of the four core virion proteins sampled across the diversity of the lineage, together with Bayesian and maximum-likelihood hypothesis-testing methods, and estimate rooted phylogenies. We find strong evidence that adenoviruses and NCLDVs are not sister groups, and thatMavericksand Mavirus acquired the rve-integrase independently. We also found strong support for a monophyletic group of virophages (familyLavidaviridae) and a most likely root placed between virophages and the other lineages. Our observations support alternatives to the nuclear-escape scenario and a billion years evolutionary arms-race between virophages and NCLDVs.