  Networks growing according to the rule that every new node has a probability
p_k of being attached to k preexisting nodes, have a universal phase diagram
and exhibit power law decays of the distribution of cluster sizes in the
non-percolating phase. The percolation transition is continuous but of infinite
order and the size of the giant component is infinitely differentiable at the
transition (though of course non-analytic). At the transition the average
cluster size (of the finite components) is discontinuous.
