This paper explores the character of hegemony in world politics today through an examination of the so-called ‘IANA stewardship transition’ of 2014-16. What does this reconstruction of global Internet governance reveal about the contemporary workings of hegemony (understood as legitimated rule by dominant power)? The IANA transition suggests a ‘complex’ hegemony with several key co-constituting aspects: both state and nonstate actors together with both material and ideational structures. Regarding states, the IANA transition reveals reduced though still notable legitimated dominance of the United States Government (USG) in global Internet governance. Yet the relative USG retreat has not thus far made way for another hegemonic state, but rather for increased hegemony of a transsectoral global elite network, self-designated as ‘the multistakeholder community’ (MSC). The USG and the MSC gained strength in the IANA transition by their substantial co-dependence, although their combined hegemony, too, has significant limitations. Fuller hegemony in global Internet governance has been achieved when these actors have interconnected with the legitimated dominance of certain deeper social structures. On the one hand, forces of capitalism have constituted a hegemonic material structure in the IANA transition, with surplus accumulation being widely embraced as a dominant ordering principle for the world digital economy. On the other hand, and partly compensating for limits to capitalist hegemony, a set of legitimating discourses (i.e. around security, market, multistakeholder, accountability, public interest, and human rights) have injected considerable ideational structure into the mix of complex hegemony. While none of USG, MSC, capitalism or discourse is sufficient by itself to yield legitimated dominance in today’s global Internet governance, together they form a powerful hegemonic combination. Yet even this four-faceted complex hegemony is fragile to the extent that each aspect faces significant delegitimating critiques. Moreover, the regime’s legitimacy so far rests mainly on a narrow elite base. This underlying instability suggests that the post-transition future can bring further change in global Internet governance, albeit in directions that are as yet unclear.