I need to change the thickness and color of all the borders of all the tables of a document at once. Is it possible ?
I have tried selecting a cell and then editing the Table Contents style. It adds more borders inside the already existing cell… I can’t seem to find the correct style to edit.
No, it’s not possible, sorry. Table borders are different from paragraph style borders and that’s why when you add a border to the paragraph style you get nested borders.
As Regina says on a different thread table styles are far from being complete. Maybe someone with enough expertise will be able to write a macro that goes from table to table changing its properties, but I thinks this is one of those cases on which an automated solution will take more effort than old school manual work.
So, grab some coffee 
Thanks, I’m suprised LibreOffice can’t do that… I will follow your advice and grab some coffee 