  For the class of free-infinitely divisible transforms are introduced three
families of increasing Urbanik type subclasses of those transforms. They begin
with the class of free-normal transforms and end up with the whole class of
free-infinitely divisible transforms. Those subclasses are derived from the
ones of classical infinitely divisible measures for which are known their
random integral representations. Special functions like Hurwitz-Lerch,
polygamma and hypergeometric appeared in kernels of the corresponding integral
representations.
