Hi, Pt-
First, thank you for your answer,
I have done the analysis and:

Re. "Since I increase the number of regions and so the number of subdivisions in each atlas I may expect a relatively linear increase of the mean ReHo for each atlas?"*
Re. "Does this will really identify an atlas that could be 'ideal' for a correlation matrix analysis?"

--Yes, the increase is really linear and it actually doesn't allow the identification of an atlas with interesting homogenous properties.

In my view, how you equate ROIs across the different ICA splits seems harder-- inherently, at each level you will have a different number of ROIs, so how will you track the splits?

In the first place, I didn't track the split but average the ReHo score of all the regions of a given atlas.
I was thinking of creating a script that allows the tacking of the split, based on the overlap score of a given component of an ICAn and an ICAn+1. However, it is very time consuming and since the first step is not very interesting I will stop here.

Thank you again!

Clément