In domestication research, the concepts of agency and social relations are fundamental (Haddon, 2016). Studies over three decades have unraveled the complexity of how users integrate media into everyday life in both domestic and non-domestic settings, and how the social context in different ways shape domestication (Martínez & Olsson, 2020). However, the analysis of agency and social relations in domestication processes can be further developed and systematized. This paper uses the concept of transaction - central within relational sociology (Dépelteau, 2015) - to understand how agents influence each other in multifold ways during the first phase of the domestication process, namely the phase of appropriation. Drawing on interviews with 22 elderly Swedes (70 to 94 years) the paper develops a typology of appropriation processes, which is based on the various ways in which the appropriator (the one who acquires a digital device or application) and agents in his/her social context transact during appropriation. The paper identifies a continuum from self-conducted inspired appropriation over to other-conducted enforced appropriation. In the first case, the appropriator is influenced by media use in his/her social context and conducts the consumption and installation process. In the last case, actors in the social context have identified perceived needs and force the appropriator to adopt digital media by managing the consumption process, the installation and the initial learning process. Between these extremes, there are other forms of appropriation processes which are explored in the paper. The paper, hence, contributes to our understanding of how agency is played out in different ways in domestication of digital media, with a specific focus on how appropriation is driven by social transactions. The paper discusses how these social transactions can be understood as power relations, and how they also can be seen as vehicles for digitalization and digital inclusion.