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You should be able to get the routed data through extension method to RequestContext that resides in namespace EPiServer.Web.Routing:
var newsContent = Request.RequestContext.GetRoutedData<NewsContent>();
I have configured a partial route in a website which is using web form templates.
I have followed the tutorial on partial routing and am able to register a partial route which correctly loads my aspx template when the route is matched.
http://sdkbeta.episerver.com/SDK-html-Container/?path=/SdkDocuments/CMS/7/Knowledge%20Base/Developer%20Guide/Partial%20Routing/News%20partial%20routing%20example.htm&vppRoot=/SdkDocuments//CMS/7/Knowledge%20Base/Developer%20Guide/
I dont know the best way to access the custom route data from within the web form template.
Following the example in the SDK, if I where to create a webforms template to display a "NewsContent" item, the code behind I would look like this.
The code for accessing the route data works but is this correct / the best way? If this was a page, I would inherit TemplatePage<T> which gives typed access to the model, however I cannot do that here as NewsContent is not a page in the CMS.
Adam