Setting BorderThickness to "0" will not work here. Though it removes all borders, still the shadow effect persists. To get around this, use the control templates.

Code:
<Style  TargetType="{x:Type TabControl}">
            <Setter Property="OverridesDefaultStyle" Value="True" />
            <Setter Property="SnapsToDevicePixels" Value="True" />
            <Setter Property="Template">
                <Setter.Value>
                    <ControlTemplate TargetType="{x:Type TabControl}">
                        <Grid KeyboardNavigation.TabNavigation="Local">
                            <Grid.RowDefinitions>
                                <RowDefinition Height="Auto"/>
                                <RowDefinition Height="*"/>
                            </Grid.RowDefinitions>
                            <TabPanel 
              Name="HeaderPanel"
              Grid.Row="0"
              Panel.ZIndex="1" 
              Margin="0,0,4,-1" 
              IsItemsHost="True"
              KeyboardNavigation.TabIndex="1"
              Background="Transparent" />
                            <Border 
              Name="Border" 
              Grid.Row="1" 
              Background="White" 
              BorderBrush="Transparent" 
              BorderThickness="1" 
              CornerRadius="2" 
              KeyboardNavigation.TabNavigation="Local"
              KeyboardNavigation.DirectionalNavigation="Contained"
              KeyboardNavigation.TabIndex="2" >
                                <ContentPresenter 
                Name="PART_SelectedContentHost"
                Margin="4"
                ContentSource="SelectedContent" />
                            </Border>
                        </Grid>
                        <ControlTemplate.Triggers>
                            <Trigger Property="IsEnabled" Value="False">
                                <Setter Property="Foreground" Value="Gray" />
                                <Setter TargetName="Border" Property="BorderBrush" Value="Transparent" />
                            </Trigger>
                        </ControlTemplate.Triggers>
                    </ControlTemplate>
                </Setter.Value>
            </Setter>
        </Style>
Inspect the code, remove/add as per your requirement.

Put this code in the App.xaml file.
This will remove all the borders from the tab control.

You may also create a seperate resource file for a control template and add the reference of it in the App.xaml file.

Try this.. it will surely work.