  Understanding how young stars gain their masses through disk-to-star
accretion is of paramount importance in astrophysics. It affects our knowledge
about the early stellar evolution, the disk lifetime and dissipation processes,
the way the planets form on the smallest scales, or the connection to
macroscopic parameters characterizing star-forming regions on the largest ones,
among others. In turn, mass accretion rate estimates depend on the accretion
paradigm assumed. For low-mass T Tauri stars with strong magnetic fields there
is consensus that magnetospheric accretion (MA) is the driving mechanism, but
the transfer of mass in massive young stellar objects with weak or negligible
magnetic fields probably occurs directly from the disk to the star through a
hot boundary layer (BL). The intermediate-mass Herbig Ae/Be (HAeBe) stars
bridge the gap between both previous regimes and are still optically visible
during the pre-main sequence phase, thus constituting a unique opportunity to
test a possible change of accretion mode from MA to BL. This review deals with
our estimates of accretion rates in HAeBes, critically discussing the different
accretion paradigms. It shows that although mounting evidence supports that MA
may extend to late-type HAes but not to early-type HBes, there is not yet a
consensus on the validity of this scenario versus the BL one. Based on MA and
BL shock modeling, it is argued that the ultraviolet regime could significantly
contribute in the future to discriminating between these competing accretion
scenarios.
