  It is shown that in a subcritical random graph with given vertex degrees
satisfying a power law degree distribution with exponent $\gamma>3$, the
largest component is of order $n^{1/(\gamma-1)}$. More precisely, the order of
the largest component is approximatively given by a simple constant times the
largest vertex degree. These results are extended to several other random graph
models with power law degree distributions. This proves a conjecture by
Durrett.
