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With the advent of ALMA, it is now possible to observationally constrain how discs form around deeply embedded protostars. In particular, the recent ALMA C3H2 line observations of the nearby protostar L1527 have been interpreted as evidence for the so-called ‘centrifugal barrier,’ where the protostellar envelope infall is gradually decelerated to a stop by the centrifugal force in a region of super-Keplerian rotation. To test the concept of centrifugal barrier, which was originally based on angular momentum conserving-collapse of a rotating test particle around a fixed point mass, we carry out simple axisymmetric hydrodynamic simulations of protostellar disc formation including a minimum set of ingredients: self-gravity, rotation, and a prescribed viscosity that enables the disc to accrete. We find that a super-Keplerian region can indeed exist when the viscosity is relatively large but, unlike the classic picture of centrifugal barrier, the infalling envelope material is not decelerated solely by the centrifugal force. The region has more specific angular momentum than its surrounding envelope material, which points to an origin in outward angular momentum transport in the disc (subject to the constraint of disc expansion by the infalling envelope), rather than the spin-up of the envelope material envisioned in themore »classic picture as it falls closer to the centre in order to conserve angular momentum. For smaller viscosities, the super-Keplerian rotation is weaker or non-existing. We conclude that, despite the existence of super-Keplerian rotation in some parameter regime, the classic picture of centrifugal barrier is not supported by our simulations.