Twitter includes aspects of both an online social network and an information-distribution network. Our focus is the latter. Because Twitter provides a low-cost mechanism for users to rewire links, we can expect the dynamic activity of optimizing link structures for the comfortable viewing of information. When tracking the chronological changes in the links of sampled users, we found a phenomenon in which users with more than 32 outbound links tended to connect to nodes with a middle-sized degree, although they first preferred to follow celebrities. We call this behavioural pattern decentralising attachment, which characterises flow-type media, where information is pushed to subscribers. When a high-degree node grows and acquires more links, information from it can easily be obtained from various routes. If the information- diffusion speed is fast enough, the value of direct links to high-degree nodes will decrease, and links to secondary senders who select information for the specific subscribers will become more important. Through a simulation based on the decentralising attachment, we explain the gentle and curved slope of the degree distribution found in Twitter. In addition, we found that frequent rewiring has the effect of impeding the growth of a high-degree node. In cooperation with mechanisms to guide users to a higher-degree node, decentralising attachment forms a network topology adapted to a collaborative filtering function for information diffusion. We believe that the proposed model will contribute to the design of future social media.