  The star $\beta$ Pictoris harbors a young planetary system, which is
characterized by the presence of a gaseous and dusty debris disk, at least two
massive planets and many minor bodies. For more than thirty years, exocomets
transiting the star have been detected using spectroscopy, probing the gaseous
part of the cometary comas and tails.
  The detection of the dusty component of the tails can be performed through
photometric observations of the transits. Since 2018, the Transiting Exoplanet
Survey Satellite has observed $\beta$ Pic for a total of 156 days. Here we
report an analysis of the TESS photometric data set with the identification of
a total of 30 transits of exocomets. Our statistical analysis shows that the
number of transiting exocomet events ($N$) as a function of the absorption
depth ($AD$) in the light curve follows a power law in the form $dN(AD) \propto
AD^{-\alpha}$, where $\alpha=2.3\pm 0.4$. This distribution of absorption depth
leads to a differential comet size distribution proportional to $R^{-\gamma}$,
where $\gamma =3.6 \pm 0.8$, showing a striking similarity to the size
distribution of comets in the Solar system and the distribution of a
collisionally relaxed population ($\gamma_{\rm D}= 3.5$).
