Angular injectors (generally) return singletons. That is, in the previous example, all components in the application will receive the same random number. In AngularJS there was only one injector, and all services were singletons. Angular overcomes this limitation by using a tree of injectors.
In Angular there is not just one injector per application, there is at least one injector per application. Injectors are organized in a tree that parallels Angular's component tree.
Consider the following tree, which models a chat application consisting of two open chat windows, and a login/logout widget.
Image of a Component Tree, and a DI Tree
In the image above, there is one root injector, which is established through @NgModule's providers array. There's a LoginService registered with the root injector.
Below the root injector is the root @Component. This particular component has no providers array and will use the root injector for all of its dependencies.
There are also two child injectors, one for each ChatWindow component. Each of these components has their own instantiation of a ChatService.
There is a third child component, Logout/Login, but it has no injector.
There are several grandchild components that have no injectors. There are ChatFeed and ChatInput components for each ChatWindow. There are also LoginWidget and LogoutWidget components with Logout/Login as their parent.
The injector tree does not make a new injector for every component, but does make a new injector for every component with a providers array in its decorator. Components that have no providers array look to their parent component for an injector. If the parent does not have an injector, it looks up until it reaches the root injector.
Warning: Be careful with provider arrays. If a child component is decorated with a providers array that contains dependencies that were also requested in the parent component(s), the dependencies the child receives will shadow the parent dependencies. This can have all sorts of unintended consequences.