C# :: WPF Cascading DataContext Like With DataGrid?

I'm trying to create custom WPF control, similar to DataGrid. DataGrid was great as a base class for a different custom control I needed, because I could do something like this:

<shared:MyDataGrid ItemsSource="{Binding Persons}" >
<DataGrid.Columns>
<DataGridTextColumn Binding="{Binding Name}" Width="4*" />
<DataGridTextColumn Binding="{Binding Phone}" Width="3*" />
<DataGridTextColumn Binding="{Binding Email}" Width="3*" />
</DataGrid.Columns>
</shared:MyDataGrid>

where Person class would be like this:

public class Person
{
public string Name {get; set;}
public string Phone {get; set;}
public string Email {get; set;}
}

... and I can reuse it elsewhere with collections of different type, binding its properties to columns of different width and style.

What I need now is something similar, but differs in a way, that DataGrid is no longer good fit for the base class.

What I'm interested in is: how does DataGrid "tell" the columns in Columns collection, to have the type of ItemsSource bound collection as a DataContext? How does the Name property of Person class become available to the column in DataGrid.Columns?