Dependency parsing is a crucial step towards deep language understanding and, therefore, widely demanded by numerous Natural Language Processing applications. In particular, left-to-right and top-down transition-based algorithms that rely on Pointer Networks are among the most accurate approaches for performing dependency parsing. Additionally, it has been observed for the top-down algorithm that Pointer Networks’ sequential decoding can be improved by implementing a hierarchical variant, more adequate to model dependency structures. Considering all this, we develop a bottom-up oriented Hierarchical Pointer Network for the left-to-right parser and propose two novel transition-based alternatives: an approach that parses a sentence in right-to-left order and a variant that does so from the outside in. We empirically test the proposed neural architecture with the different algorithms on a wide variety of languages, outperforming the original approach in practically all of them and setting new state-of-the-art results on the English and Chinese Penn Treebanks for non-contextualized and BERT-based embeddings.