As witnessed by several authors (see for example Nachmias, Peres [2008], Riordan-Wormald [2010]), Addagio-Berry, Broutin, Goldschmidt [2010]) studying extremal properties (diameter, circumference, longuest path, maximum block size, …) of Erd\H os-Rényi random graphs $G(n, M)$ (resp. $G(n, p)$) appear to be extremely difficult inside its critical window of transition. That is as the number of edges satisfies $M=n/2+x n^{2/3}$ (resp. $p=1/n + x/n^{4/3}$) for $x=O(1)$. In this talk, I will show how generating function approach can capture the maximum block size and give explicit bounds for the other parameters (as functions of $x$).