  The Norros-Reittu model is a random graph with $n$ vertices and i.i.d.
weights assigned to them. The number of edges between any two vertices follows
an independent Poisson distribution whose parameter is increasing in the
weights of the two vertices. Choosing a suitable weight distribution leads to a
power-law behaviour of the degree distribution as observed in many real-world
complex networks. We study this model in the subcritical regime, i.e. in the
absence of a giant component. For each component, we count the vertices and
show convergence of the corresponding point process to a Poisson process. More
generally, one can also count only specific vertices per component, like
leaves. From this one can deduce asymptotic results on the size of the largest
component or the maximal number of leaves in a single component. The results
also apply to the Chung-Lu model and the generalised random graph.
