App.js

import relayNestedRoutes from 'relay-nested-routes';

const NestedRootContainer = relayNestedRoutes(React, Relay);

React.render(
  <Router history={new BrowserHistory()}>
    <Route component={NestedRootContainer}>
      <Route
        name="home" // added a name to the route
        path="/"
        component={App}
        queries={HomeQueries} // and the query
      />
      <Route
        name="widget"
        path="/widget/:id"
        component={Widget}
        queries={WidgetQueries}
      />
    </Route>
  </Router>,
  document.getElementById('root')
);

I think the only change this needs for the new react-router-relay API is just the top-level ReactRouterRelay.createElement on the Router rather than the NestedRootContainer.