Abstract: Context: Broad absorption line quasars (BAL QSOs) belong to a class of objects not well-understood as yet. Their UV spectra show BALs in the blue wings of the UV resonance lines, owing to ionized gas with outflow velocities up to 0.2 c. They can have radio emission that is difficult to characterize and that needs to be studied at various wavelengths and resolutions. Aims: We aim to study the pc-scale properties of their synchrotron emission and, in particular, to determine their core properties. Methods: We performed observations in the Very Long Baseline Interferometry (VLBI) technique, using both the European VLBI Network (EVN) at 5 GHz, and the Very Long Baseline Array (VLBA) at 5 and 8.4 GHz to map the pc-scale structure of the brightest radio-loud objects of our sample, allowing a proper morphological interpretation. Results: A variety of morphologies have been found: 9 BAL QSOs on a total of 11 observed sources have a resolved structure. Core-jet, double, and symmetric objects are present, suggesting different orientations. In some cases the sources can be young GPS or CSS. The projected linear size of the sources, also considering observations from our previous work for the same objects, can vary from tens of pc to hundreds of kpc. In some cases, a diffuse emission can be supposed from the missing flux-density with respect to previous lower resolution observations. Finally, the magnetic field strength does not significantly differ from the values found in the literature for radio sources with similar sizes. Conclusions: These results are not easily interpreted with the youth scenario for BAL QSOs, in which they are generally compact objects still expelling a dust cocoon. The variety of orientations, morphologies, and extensions found are presumably related to different possible angles for the BAL producing outflows, with respect to the jet axis. Moreover, the phenomenon could be present in various phases of the QSO evolution.

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