  In the infinite configuration network the links between nodes are assigned
randomly with the only restriction that the degree distribution has to match a
predefined function. This work presents a simple equation that gives for an
arbitrary degree distribution the corresponding size distribution of connected
components. This equation is suitable for fast and stable numerical
computations up to the machine precision. The analytical analysis reveals that
the asymptote of the component size distribution is completely defined by only
a few parameters of the degree distribution: the first three moments, scale and
exponent (if applicable). When the degree distribution features a heavy tail,
multiple asymptotic modes are observed in the component size distribution that,
in turn, may or may not feature a heavy tail.
