  Aims: Past observations of fast-rotating massive stars exhibiting normal
nitrogen abundances at their surface have raised questions about the rotational
mixing paradigm. We revisit this question thanks to a spectroscopic analysis of
a sample of bright fast-rotating OB stars, with the goal of quantifying the
efficiency of rotational mixing at high rotation rates. Method: Our sample
consists of 40 fast rotators on the main sequence, with spectral types
comprised between B0.5 and O4. We compare the abundances of some key element
indicators of mixing (He, CNO) with the predictions of evolutionary models for
single objects and for stars in interacting binary systems. Results: The
properties of half of the sample stars can be reproduced by single evolutionary
models, even in the case of probable or confirmed binaries that can therefore
be true single stars in a pre-interaction configuration. The main problem for
the rest of the sample is a mismatch for the [N/O] abundance ratio (we confirm
the existence of fast rotators with a lack of nitrogen enrichment) and/or a
high helium abundance that cannot be accounted for by models. Modifying the
diffusion coefficient implemented in single- star models does not solve the
problem as it cannot simultaneously reproduce the helium abundances and [N/O]
abundance ratios of our targets. Since part of them actually are binaries, we
also compared their chemical properties with predictions for post-mass transfer
systems. We found that these models can explain the abundances measured for a
majority of our targets, including some of the most helium-enriched, but fail
to reproduce them in other cases. Our study thus reveals that some physical
ingredients are still missing in current models.
