We present our contribution to The First Shared Task on Extrinsic Parser Evaluation (EPE 2017). Our participant system, the UDPipe, is an open-source pipeline performing tokenization, morphological analysis, part-of-speech tagging, lemmatization and dependency parsing. It is trained in a language agnostic manner for 50 languages of the UD version 2. With a relatively limited amount of training data (200k tokens of English UD) and without any English specific tuning, the system achieves overall score 56.05, placing as the 7th participant system.