Applies to TabControl and TabItem. Three groups: the underline that marks the selected tab, the animation when the content changes, and closable tabs.
The underline

| Property | Type | Default | |
|---|---|---|---|
Underlined |
UnderlinedType |
None |
what gets an underline |
UnderlinePlacement |
Dock? |
null |
which side of the tab it sits on |
UnderlineBrush |
Brush |
null |
under an unselected tab |
UnderlineSelectedBrush |
Brush |
null |
under the selected tab |
UnderlineMouseOverBrush |
Brush |
null |
under a tab the pointer is over |
UnderlineMouseOverSelectedBrush |
Brush |
null |
under the selected tab, pointer over it |
UnderlinedType has four values. None is the default and draws nothing; TabItems underlines every tab; SelectedTabItem underlines only the selected one; TabPanel draws a line under the whole strip and a coloured one under the selected tab.
<TabControl mah:TabControlHelper.Underlined="SelectedTabItem"
mah:TabControlHelper.UnderlineSelectedBrush="{DynamicResource MahApps.Brushes.Accent}" />
UnderlinePlacement moves it — Top puts the marker above the tab rather than below it, which is the older look:

Set Underlined on the TabControl and it reaches the items; setting it on a single TabItem underlines just that one.
Transitions
| Property | Type | Default | |
|---|---|---|---|
Transition |
TransitionType |
Default |
the animation when the selected tab changes |
TransitionType is Default, Normal, Up, Down, Right, RightReplace, Left, LeftReplace or Custom. It is the same enum the TransitioningContentControl uses, because that is what draws the content.
<TabControl mah:TabControlHelper.Transition="Left" />
Closable tabs
| Property | Type | Default | |
|---|---|---|---|
CloseButtonEnabled |
bool |
false |
show a close button on the tab |
CloseTabCommand |
ICommand |
null |
invoked when it is clicked |
CloseTabCommandParameter |
object |
null |
passed to that command |
These three are only read by the Visual Studio tab styles — MahApps.Styles.TabControl.VisualStudio and MahApps.Styles.TabItem.VisualStudio in Styles/VS/TabControl.xaml, which Controls.xaml does not merge. On a tab control with the ordinary styles they have no effect at all.
Merge the dictionary and apply the styles to use them:
<ResourceDictionary Source="pack://application:,,,/MahApps.Metro;component/Styles/VS/TabControl.xaml" />
<TabControl Style="{StaticResource MahApps.Styles.TabControl.VisualStudio}"
ItemContainerStyle="{StaticResource MahApps.Styles.TabItem.VisualStudio}"
mah:TabControlHelper.CloseTabCommand="{Binding CloseTabCommand}" />
The VS tab item style sets CloseButtonEnabled to True itself, so the button is there as soon as the style is.
For a closable tab without the Visual Studio look, use MetroTabItem instead — it has its own CloseButtonEnabled property, unrelated to this helper.
Related
HeaderedControlHelper styles the tab strip's header. See HeaderedControlHelper.