Different aspects of EEG Data are shared in different formats:
Raw EEG: continuous EEG recordings alongside behavioural data in BIDS format. Note that raw anaesthesia data can be downloaded here: https://zenodo.org/record/806176#.YURO9dMzZR4
Preprocessed EEG: Epoched EEG recordings alongside behavioural data in .mat (fieldtrip) format.
ERPs: Condition-wise average ERPs per participant in .mat (fieldtrip) format.
Spectra: Trial-wise power spectral densities per participant in .mat format.
Spectral parameterization results: Results of trial-wise spectral parameterization (including goodness of fit) per participant in .mat format.