Auto - The sizing grip is only shown when the form is sizable (ie has Form.FormBorderStyle set to FormBorderStyle.Sizable or FormBorderStyle.SizableToolWindow) and is shown as a dialog via a call to Form.ShowDialog().
Hide - The sizing grip is never shown.
Show - The sizing grip is always shown as long as the form is sizable (ie has Form.FormBorderStyle set to FormBorderStyle.Sizable or FormBorderStyle.SizableToolWindow).