Multi-participant discussions tend to unfold in a tree structure rather than a chain structure. Branching may occur for multiple reasons -- from the asynchronous nature of online platforms to a conscious decision by an interlocutor to disengage with part of the conversation. Predicting branching and understanding the reasons for creating new branches is important for many downstream tasks such as summarization and thread disentanglement and may help develop online spaces that encourage users to engage in online discussions in more meaningful ways. In this work, we define the novel task of branch prediction and propose GLOBS (Global Branching Score) -- a deep neural network model for predicting branching. GLOBS is evaluated on three large discussion forums from Reddit, achieving significant improvements over an array of competitive baselines and demonstrating better transferability. We affirm that structural, temporal, and linguistic features contribute to GLOBS success and find that branching is associated with a greater number of conversation participants and tends to occur in earlier levels of the conversation tree. We publicly release GLOBS and our implementation of all baseline models to allow reproducibility and promote further research on this important task.