  Let ccl(G) denote the order of the largest complete minor in a graph G (also
called the contraction clique number) and let G(n,p) denote a random graph on n
vertices with edge probability p. Bollobas, Catlin and Erdos asymptotically
determined ccl(G (n,p)) when p is a constant. Luczak, Pittel and Wierman gave
bounds on ccl(G(n,p)) when p is very close to 1/n, i.e. inside the phase
transition. Extending the results of Bollobas, Catlin and Erdos, we determine
ccl(G(n,p)) quite tightly, for p>C/n where C is a large constant. If p=C/n, for
an arbitrary constant C>1, then we show that asymptotically almost surely ccl(G
(n,p)) is of order square-root of n. This answers a question of Krivelevich and
Sudakov.
