We consider the limit distribution of the orders of the $k$ largest components in the Erdos-Rényi random graph inside the "critical window" for arbitrary $k$. We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function.
"A local limit theorem for the critical random graph." Electron. Commun. Probab. 14 122 - 131, 2009. https://doi.org/10.1214/ECP.v14-1451