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In a pair of artificial language experiments, we investigated the learnability and emergence of different dependency structures: branching, center-embedding, and crossed. In natural languages, branching is the most common dependency structure; center-embedding occurs but is often disfavored, and crossed dependencies are very rare. Experiment 1 addressed learnability, testing comprehension, and production on small artificial languages exemplifying each dependency type in noun phrases. As expected, branching dependency grammars were the easiest to learn, but crossed grammars were not different from center-embedding. Experiment 2 employed iterated learning to examine the emergence and stabilization of consistent grammar using the same type of stimuli as Experiment 1. The initial participant in each chain of transmission was trained on phrases generated by a random grammar, with the language produced by that participant passed to the next participant through an iterated learning process. Branching dependency grammar appeared in most chains within a few generations and remained stable once it appeared, although one chain stabilized on output consistent with a crossed grammar; no chains converged on center-embedding grammars. These findings, along with some previous results, call into question the assumption that crossed dependencies are more cognitively complex than center-embedding, while confirming the role of learnability in the typology of dependency structures.