This paper offers an analytical framework to critically examine the power relations that structure the online platform ecosystem. Following a relational understanding of power, it focuses on the connections between the five leading platform corporations - Alphabet-Google, Apple, Facebook, Amazon, and Microsoft (GAFAM) - and the many other digital properties (i.e. platforms, websites, and apps) that populate the online ecosystem. Exploring these connections, we notice that a growing number of digital properties are integrated with, and increasingly dependent on the infrastructural services offered by the GAFAM platforms. These services include: advertising networks, login services, cloud hosting, app stores, payment systems, data analytics, video hosting, geospatial and navigation services, search functionalities, and operating systems. Such infrastructural services allow a wide variety of companies to make their products and services available online, attract and target users, analyze their activities, and generate revenue. It is through the ubiquitous integration and consistent use of these infrastructural services that platform power emerges and is consolidated. To demonstrate how such power relations can be analyzed, the paper highlights two key infrastructural services: app stores and ad networks. For each service it discusses two levels of analysis that can be pursued to gain insight in the workings of platform power. Ultimately a systematically analysis of the key infrastructural services will need to be developed to arrive at a refined taxonomy of platform power relations. Such taxonomy is essential to establish guidelines for governing the platform ecosystem in correspondence with key public values.