AbstractA random mapping (T; q) of a finite setV= {1, 2,…,n} into itself assigns independently to eachiϵVits unique imagej=TT(i)E Vwith probabilityqfori=jand with probability\documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{1 - q}}{{n - 1}} $\end{document}forj≠i. The purpose of the article is to determine the asymptotic behaviour of the size of the largest connected component of the random digraphGT(q)representing thes mapping asn–x, regarding all possible values of the parameterq=q(n). © 1994 John Wiley&So