This paper presents an approach of automatic annotation of sentences with dependency structures. The approach builds on the idea of cross-lingual dependency projection. The presented method of acquiring dependency trees involves a weighting factor in the processes of projecting source dependency relations to target sentences and inducing well-formed target dependency trees from sets of projected dependency relations. Using a parallel corpus, source trees are transferred onto equivalent target sentences via an extended set of alignment links. Projected arcs are initially weighted according to the certainty of word alignment links. Then, arc weights are recalculated using a method based on the EM selection algorithm. Maximum spanning trees selected from EM-scored digraphs and labelled with appropriate grammatical functions constitute a target dependency treebank. Extrinsic evaluation shows that parsers trained on such a treebank may perform comparably to parsers trained on a manually developed treebank.