The sitemap is a soul of a website. Or you can say it's the extract of the whole website submitted to the search engine to crawl. The ideal sitemap will helpful in indexing site more efficiently. The bots from a search engine will automatically learn/crawl the website through a sitemap. Most sitemaps are in XML format. However, you can add it in a readable format for users, often found in HTML format.
Anyway, come to the point, submitting and nurturing depends solely on preferred domain choice. This means when you favor a non-www version of a domain then submit the sitemap for a non-www version only. Alternatively, you need to delink sitemap for other versions.
For example. In the past, I was using http://www.example.com and submitted a sitemap for the same. Now, I opted for http://example.com. So, I should submit a new sitemap for non-www version and delink a sitemap with www domain.
You can get official Google information on Google Webmaster Support
