This is a sequel to the question: https://mathoverflow.net/questions/299253/proof-and-interpretation-of-the-following-percolation-theory-result-for-n-times

In the paper: [The Birth of the Infinite Cluster:¶Finite-Size Scaling in Percolation](https://link.springer.com/article/10.1007%2Fs002200100521)

> Theorem 3.2 basically states that with probability going to $1$ as
> $n\rightarrow\infty$, the largest open cluster in an $n\times n$ box
> is of size $\theta(p)n^2$, $\theta(p)$ being the percolation
> probability.

This result is for bond percolation. However, does there exist any analogous result for site percolation?