It is well-known from work by Kesten in the mid-eighties and work by Borgs, Chayes, Kesten and Spencer around 2000 that, informally speaking, the largest, the second largest, the third largest etcetera cluster in an $n$ times $n$ box in 2D critical percolation typically have size of order $n^2 \pi(n)$. Here $\pi(n)$ is the probability that a given vertex v has an open path to vertices at distance at least $n$ from v. Motivated by so-called frozen percolation problems (which I will briefly explain), we obtained some new modifications/refinements of these results. I will also address our work on an open problem in this area posed in a paper by Jarai (2003). Part of this talk is based on joint work with R. Conijn and D. Kiss.