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Multi-target regression is concerned with the prediction of multiple continuous target variables using a shared set of predictors. Two key challenges in multi-target regression are: (a) modelling target dependencies and (b) scalability to large output spaces. In this paper, a new multi-target regression method is proposed that tries to jointly address these challenges via a novel problem transformation approach. The proposed method, called MRQ, is based on the idea of quantizing the output space in order to transform the multiple continuous targets into one or more discrete ones. Learning on the transformed output space naturally enables modeling of target dependencies while the quantization strategy can be flexibly parameterized to control the trade-off between prediction accuracy and computational efficiency. Experiments on a large collection of benchmark datasets show that MRQ is both highly scalable and also competitive with the state-of-the-art in terms of accuracy. In particular, an ensemble version of MRQ obtains the best overall accuracy, while being an order of magnitude faster than the runner up method.