Although humans live in an open-ended world and endlessly face new challenges, they do not have to learn from scratch each time they face the next one. Rather, they have access to a handful of previously learned skills, which they rapidly adapt to new situations. In artificial intelligence, autotelic agents-which are intrinsically motivated to represent and set their own goals-exhibit promising skill adaptation capabilities. However, these capabilities are highly constrained by their policy and goal space representations. In this paper, we propose to investigate the impact of these representations on the learning and transfer capabilities of autotelic agents. We study different implementations of autotelic agents using four types of Graph Neural Networks policy representations and two types of goal spaces, either geometric or predicate-based. By testing agents on unseen goals, we show that combining object-centered architectures that are expressive enough with semantic relational goals helps learning to reach more difficult goals. We also release our graph-based implementations to encourage further research in this direction.