  In this article the relation between the tail behaviours of a free regular
infinitely divisible (positively supported) probability measure and its L\'evy
measure is studied. An important example of such a measure is the compound free
Poisson distribution, which often occurs as a limiting spectral distribution of
certain sequences of random matrices. We also describe a connection between an
analogous classical result of Embrechts et al. [1979] and our result using the
Bercovici-Pata bijection.
