  We prove existence and asymptotic behavior of the transition density for a
large class of subordinators whose Laplace exponents satisfy lower scaling
condition at infinity. Furthermore, we present lower and upper bounds for the
density. Sharp estimates are provided if additional upper scaling condition on
the Laplace exponent is imposed. In particular, we cover the case when the
(minus) second derivative of the Laplace exponent is a function regularly
varying at infinity with regularity index bigger than -2.
