What is...a higher dimensional stable family?                                                                    
-- Sándor Kovács, November 12, 2010

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I will discuss issues and difficulties that arise when one
attempts to define stable families of higher dimensional
varieties and some recent related results.  These will include
a relevant consequence of joint work of Koll&aacute;r and myself and
a related question of Koll&aacute;r answered recently by Patakfalvi.