  We aim to explore two exozodiacal dust production mechanisms, first
re-investigating the Poynting-Robertson drag pile-up scenario, and then
elaborating on the less explored, but promising exocometary dust delivery
scenario. We developped a new versatile, numerical model that calculates the
dust dynamics, with non orbit-averaged equations for the grains close to the
star. The model includes dust sublimation and incorporates a radiative transfer
code for direct comparison to the observations. We consider in this study four
stellar types, three dust compositions, and we assume a parent belt at 50 au.
We find that, in the case of the Poynting-Robertson drag pile-up scenario, it
is impossible to produce long-lived submicron-sized grains close to the star.
The inward drifting grains fill in the region between the parent belt and the
sublimation distance, producing an unrealistically strong mid-infrared excess
compared to the near-infrared excess. The dust pile-up at the sublimation
radius is by far insufficient to boost the near-IR flux of the exozodi to the
point where it dominates over the mid-infrared excess. In the case of the
exocometary dust delivery scenario, we find that a narrow ring can form close
to the sublimation zone, populated with large grains several tens to several
hundred of micrometers in radius. Although not perfect, this scenario provides
a better match to the observations, especially if the grains are carbon-rich.
We also find that the required number of active exocomets to sustain the
observed dust level is reasonable. We conclude that the hot exozodiacal dust
detected by near-infrared interferometry is unlikely to result from inwards
grains migration by Poynting-Robertson drag from a distant parent belt, but
could instead have an exocometary origin. [Abridged]
