I have to create a site with severals child sites usind Sharepoint team services. How can I set up a webpart to be shared between those sites, if a user add an event ( for exemple ), this event will appear onto all child site event's webpart.
SharePoint Team services doesn't have web parts, so presumably you have got the name worng and you are actually using Windows sharepoint Services. It's newsgroup is microsoft.public.sharepoint.windowsservices