The inception of the Relational Graph Convolutional Network (R-GCN) marked a milestone in the Semantic Web domain as a widely cited method that generalises end-to-end hierarchical representation learning to Knowledge Graphs (KGs). R-GCNs generate representations for nodes of interest by repeatedly aggregating parameterised, relation-specific transformations of their neighbours. However, in this paper, we argue that the the R-GCN's main contribution lies in this "message passing" paradigm, rather than the learned weights. To this end, we introduce the "Random Relational Graph Convolutional Network" (RR-GCN), which leaves all parameters untrained and thus constructs node embeddings by aggregating randomly transformed random representations from neighbours, i.e., with no learned parameters. We empirically show that RR-GCNs can compete with fully trained R-GCNs in both node classification and link prediction settings.