How far can we get with unsupervised parsing if we make our training corpus several orders of magnitude larger than has hitherto be attempted? We present a new algorithm for unsupervised parsing using an all-subtrees model, termed U-DOP*, which parses directly with packed forests of all binary trees. We train both on Penn’s WSJ data and on the (much larger) NANC corpus, showing that U-DOP * outperforms a treebank-PCFG on the standard WSJ test set. While U-DOP * performs worse than state-of-the-art supervised parsers on handannotated sentences, we show that the model outperforms supervised parsers when evaluated as a language model in syntax-based machine translation on Europarl. We argue that supervised parsers miss the fluidity between constituents and non-constituents and that in the field of syntax-based language modeling the end of supervised parsing has come in sight. 1