In this paper, we present our progress in pretraining Czech monolingual audio transformers from a large dataset containing more than 80 thousand hours of unlabeled speech, and subsequently fine-tuning the model on automatic speech recognition tasks using a combination of in-domain data and almost 6 thousand hours of out-of-domain transcribed speech. We are presenting a large palette of experiments with various fine-tuning setups evaluated on two public datasets (CommonVoice and VoxPopuli) and one extremely challenging dataset from the MALACH project. Our results show that monolingual Wav2Vec 2.0 models are robust ASR systems, which can take advantage of large labeled and unlabeled datasets and successfully compete with state-of-the-art LVCSR systems. Moreover, Wav2Vec models proved to be good zero-shot learners when no training data are available for the target ASR task.