Thanks for the input. Yes, sitemap does generate what I want. I found very similar scripts all around but I do not know how to initialize them beside $root_categories, which generates only the list of categories at level=0. Knowledge issue on my side. I belive:
should work if I knew what to put in place of 'categories=$root_categories'; maybe you have an input on this.
To make it short, I created a category block with appearance set to plain and put it in the home page (what I also wanted); it does the work. Too bad I cannot customize the catalog page through the admin.
Yes, very similar to views/categories/components/categories_tree.tpl.
The code does not do anything by itself; if I replace $all_categories_tree by $root_categories I get the top categories as a list. Still missing some initialization or calling code. I am not there yet.