I use angular 1.5 to develop my application and I am using .component(). I have three components and their controllers, all of which are quite similar. How can I extend the controller from comp1 to use it with comp2? 
Each component in a separate js file:
comp1.js comp2.js comp3.js
You can extend component controllers from each other as well. Use the following approach:
Parent component (to extend from):
/**
 * Module definition and dependencies
 */
angular.module('App.Parent', [])
/**
 * Component
 */
.component('parent', {
  templateUrl: 'parent.html',
  controller: 'ParentCtrl',
})
/**
 * Controller
 */
.controller('ParentCtrl', function($parentDep) {
  //Get controller
  const $ctrl = this;
  /**
   * On init
   */
  this.$onInit = function() {
    //Do stuff
    this.something = true;
  };
});
Child component (the one extending):
/**
 * Module definition and dependencies
 */
angular.module('App.Child', [])
/**
 * Component
 */
.component('child', {
  templateUrl: 'child.html',
  controller: 'ChildCtrl',
})
/**
 * Controller
 */
.controller('ChildCtrl', function($controller, $parentDep) {
  //Get controllers
  const $ctrl = this;
  const $base = $controller('ParentCtrl', {$parentDep});
  //Extend
  angular.extend($ctrl, $base);
  /**
   * On init
   */
  this.$onInit = function() {
    //Call parent init
    $base.$onInit.call(this);
    //Do other stuff
    this.somethingElse = true;
  };
});
You can define new method in the child controller, overwrite existing methods, call the parent methods, etc. Works really well.
I may suggest that you simply use services to share and compose components.  You can then skip the complexities of worrying about .extend(), $controller, etc.         
  angular
    .module('app')
    .factory('component.utils', function() {
       return {
         sharedProp: 'foo',
         sharedMethod: function() { return 'bar' }
       }
    })
    // components can all easily use functionality 
    // provided by one (or more) services, w/o 
    // needing a complicated inheritance model.
    .component('foo', {
      templateUrl: 'foo.html',
      controller: [
        'component.utils',
        function(utils) {
          this.$onInit = function() {
            this.prop = utils.sharedProp;
            utils.sharedMethod();
            // now do other foo things...
          }
        }
      ]
    })
    .component('bar', {
      templateUrl: 'foo.html',
      controller: [
        'component.utils',
        function(utils) {
          this.$onInit = function() {
            this.prop = utils.sharedProp;
            utils.sharedMethod();
            // now do other bar things...
          }
        }
      ]
    });
Inheritance has its place, but favoring composition over inheritance is usually the better solution. article.
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