The emergence of mixed human-agent societies poses challenges in designing artificial companion agents (social robots or virtual characters) that are able to form meaningful relationships with humans. We focus in particular on companion agents for children left alone at home after school while their parents are working. Problem/situations have been identified where companion agents may provide important social contact with humans. We therefore want to enable agent-human social relationships of the same form as human-human social relationships, between the child and their companions. The problematic is to determine if such companions would be acceptable by the society (in particular the children's parents), under what conditions and for what tasks. In this paper, we study the different roles that artificial companions will have to play in these various problem/situations, i.e. the behaviours expected from them in response to problems encountered by the user in a given daily life situations.