Thanks for asking this question, Allan, because it’s made me realize that I haven’t discussed this in my articles. The topics — such as family — on Medium are articles that have been curated and selected for each topic. You cannot submit your articles to them. Topics are not publications. There are lots of topics and sometimes an article will get selected for two or more (although usually they are selected for just one topic.)
Curation is done by Medium staff after you publish an article. They read the published articles and decide if they want to recommend them in a topic. You can’t submit for curation or influence it — it just happens automatically in the days/ week after you publish your story. You can get an article curated in topics regardless of whether you self-publishing or publish in a publication. Only the articles which Medium deems high quality get selected and certain topics are never curated, such as writing about Medium. Does that answer your question?