  We study the freely infinitely divisible distributions that appear as the
laws of free subordinators. This is the free analog of classically infinitely
divisible distributions supported on [0,\infty), called the free regular
measures. We prove that the class of free regular measures is closed under the
free multiplicative convolution, t-th boolean power for $0\leq t\leq 1$, t-th
free multiplicative power for $t\geq 1$ and weak convergence. In addition, we
show that a symmetric distribution is freely infinitely divisible if and only
if its square can be represented as the free multiplicative convolution of a
free Poisson and a free regular measure. This gives two new explicit examples
of distributions which are infinitely divisible with respect to both classical
and free convolutions: \chi^2(1) and F(1,1). Another consequence is that the
free commutator operation preserves free infinite divisibility.
