Creating binary tree with wpf

Question

I'm trying to create a binary tree in wpf that will look like that:

So, I created three classes - Node (Abstract), And OneTypeNode, And TwoTypeNode (those are example, btw, MVVM is important here). Every node also have reference to his two sons. in the xaml, it look something like that:

        <StackPanel>

        <Grid ShowGridLines="False">
            <Grid.ColumnDefinitions>
                <ColumnDefinition Width="1*"></ColumnDefinition>
                <ColumnDefinition Width="1*"></ColumnDefinition>
                <ColumnDefinition Width="1*"></ColumnDefinition>
            </Grid.ColumnDefinitions>
            <Grid.RowDefinitions>
                <RowDefinition></RowDefinition>
                <RowDefinition></RowDefinition>
            </Grid.RowDefinitions>

            <Border Grid.Column="1" Grid.Row="0" x:Name="CircleFather" CornerRadius="5"
                    Width="40"
                    Height="40"
                    Background="DarkKhaki" 
                                    Margin="0 20 0 0"
                    BorderThickness="1" >
            </Border>

            <ContentControl Grid.Row="2" Grid.Column="0" Content="{Binding RightSon}" Margin="10"></ContentControl>
            <ContentControl Grid.Row="2" Grid.Column="2" Content="{Binding LeftSon}" Margin="10"></ContentControl>

        </Grid>
        <Line ></Line>
    </StackPanel>

Which actually let me create sons recursively! But there are two main problems: first of all is the size, I can't control the size of the grid since I don't know how many sons are gonna be on every side. ALSO - I don't have any idea to how create the lines between every two nodes. Any idea? Thank you very very much!