Binding a Windows form to a TableAdapter through a Web Service

How can I use a TableAdapter object in a Windows Form aplication, when this TableAdapter object is returned from a Web Service? It's simple, but...

I wanted a simple thing:
1- define a TableAdapter in a Web Service project, to get a typed DataSet from the BD
2- return this TableAdater in a WebMethod
3- use the TableAdapter returned by the web service from a DataGridView in a Windows form application (referencing the web service, of course).

I tried many combinations before getting this worked, playing with objects and properties, and googling, and playing again... There is finally a recipe that works:

On the web service side:

1. Create a TableAdapter (by dragging adatabase table from the werver explorer and settinga select method). This create a DataSet (name of the *.xsd file), a DataTable (name in the top of the box) and a TableAdapter (with a "TableAdapter" suffix after the DataTable name).
   
2. Create a web method returning an instance of the new DataTable.
   

On the windows application side:

1. In the Windows client project, add a Web Reference to the class of the web service (like the default name "Service1").
   
2. Next, go on the design view of the web form. On the toolbox pane, some items are automatically added. There should be an item with the DataSet used in the web service; the name will be the "*.xsd" file name, not the DataTable or the TableAdapter name (default will be "DataSet1"). This should be in a section of the toolbox labeled with the web service namespace ("MyWebService components"). Drag this component on the web form. A DataSet object will be created.
3. Drag a BindingSource on the web form
4. In the properties of the new BindingSource object, set the datasource to the new DataSet objet. In the DataMember drop down list, you can now choose the name of the DataTable (similar to the TableAdapter name) within the DataSet.
5. In the DataGridView control properties, set the DataSource to the new DataBindingSource object.
6. All properties shoud now be ok.

To get the data populating the DataGridView on load, there is a line to write.In the Load() event of the form, add something like
Me.BindingSource1.DataSource = New [WebReferenceAliasName].[ServiceName]().[WebMethodName]()

It works fine this way.