angularjs ui-router - how to build master state which is global across app

The approach you took in your plunker is close. @ben-schwartz's solution demonstrates how you'd set defaults in your root state for the three essentially-static views. The thing missing in your plunker is that your child states still need to reference the top container view.

   .state('root',{
      url: '',
      views: {
        'header': {
          templateUrl: 'header.html',
          controller: 'HeaderCtrl'
        },
        'footer':{
          templateUrl: 'footer.html'
        }
      }
    })
    .state('root.about', {
      url: '/about',
      views: {
        'container@': {
          templateUrl: 'about.html'
        }
      }
    });    

Note views: { 'container@': ...} instead of just templateUrl: ... in 'root.about'

What you may also be asking about is whether you can have modules define their own state-sets, which you then attach to your app's state hierarchy. A sort of plug-and-play for the routes/states each module provides.

To achieve this you'll have tightly couple your modules to your main app.

In the module:

angular.module('contact', ['ui.router'])
  .constant('statesContact', [
      { name: 'root.contact',
        options: {
          url: 'contact',
          views: {
            'container@': {
              templateUrl: 'contacts.html'
            }
          },
          controller:'ContactController'
      }}
    ])
  .config(['$stateProvider', function($stateProvider){    
  }])

Then, in the app:

var app = angular.module('plunker', ['ui.router', 'contact']);
app.config(       ['$stateProvider', 'statesContact', 
           function($stateProvider,   statesContact){
    $stateProvider
    .state('root',{ ... })
    .state('root.home', { ... })
    .state('root.about', { ... })
    angular.forEach(statesContact, function(state) {
      $stateProvider.state(state.name, state.options);
    })      
}]);

This means all your modules will need to be compatible with this pattern set out in your app. But if you accept this constraint you can then choose include any combination of your modules, and their states magically get added to your app. If you want to get even fancier, you can modify state.options.url in your statesModuleName loop to, for example, prefix your module's url structure.

Also note that the module ui.compat is only necessary when you are transitioning from $routeProvider to $stateProvider. You should normally use ui.state instead.

Also don't forget to adjust in header.html $state.includes('root.contact'))

updated plunker

Although confusing, the FAQ in the ui-router wiki seems to say that this isn't possible: ui-router/wiki/faq

One approach is to allow each feature to define it's own root state (as in this example: AngularJS State Management with ui-router)

Another would be to define the entire state hierarchy in your "myApp" module and just leverage controllers etc. from the dependent modules. This works especially well when you are maintaining a mobile and desktop site; define each site's state hierarchy in a mobileApp and desktopApp module, and have the functionality (e.g. controllers, services, etc.) shared in separate modules.