Online social platforms provide a bustling arena for information-sharing and for multi-party discussions. Various frameworks for dialogic discourse parsing were developed and used for the processing of discussions and for predicting the productivity of a dialogue. However, most of these frameworks are not suitable for the analysis of contentious discussions that are commonplace in many online platforms. A novel multi-label scheme for contentious dialog parsing was recently introduced by Zakharov et al. (2021). While the schema is well developed, the computational approach they provide is both naive and inefficient, as a different model (architecture) using a different representation of the input, is trained for each of the 31 tags in the annotation scheme. Moreover, all their models assume full knowledge of label collocations and context, which is unlikely in any realistic setting. In this work, we present a unified model for Non-Convergent Discourse Parsing that does not require any additional input other than the previous dialog utterances. We fine-tuned a RoBERTa backbone, combining embeddings of the utterance, the context and the labels through GRN layers and an asymmetric loss function. Overall, our model achieves results comparable with SOTA, without using label collocation and without training a unique architecture/model for each label. Our proposed architecture makes the labeling feasible at large scale, promoting the development of tools that deepen our understanding of discourse dynamics.