Here is an illustration:
<Grid>
<TabControl>
<TabItem Header="Visible"></TabItem>
<TabItem Visibility="Hidden" Header="Hidden">Hidden</TabItem>
<TabItem Visibility="Hidden" Header="Hidden">Hidden</TabItem>
<TabItem Visibility="Hidden" Header="Hidden">Hidden</TabItem>
<TabItem Header="Visible"></TabItem>
<TabItem Header="Visible"></TabItem>
<TabItem Header="Visible"></TabItem>
</TabControl>
</Grid>
Let's do this:

And this XAML:
<Grid>
<TabControl>
<TabItem Header="Visible"></TabItem>
<TabItem Visibility="Collapsed" Header="Collapsed">Collapsed</TabItem>
<TabItem Visibility="Collapsed" Header="Collapsed">Collapsed</TabItem>
<TabItem Visibility="Collapsed" Header="Collapsed">Collapsed</TabItem>
<TabItem Header="Visible"></TabItem>
<TabItem Header="Visible"></TabItem>
<TabItem Header="Visible"></TabItem>
</TabControl>
</Grid>
You will see the following:

So, it Collapsedwill not save space, while it Hiddenwill.
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