  We study the component structure in random intersection graphs with tunable
clustering, and show that the average degree works as a threshold for a phase
transition for the size of the largest component. That is, if the expected
degree is less than one, the size of the largest component is a.a.s. of
logarithmic order, but if the average degree is greater than one, a.a.s. a
single large component of linear order emerges, and the size of the second
largest component is at most of logarithmic order.

Probability