Mel Gibson threatened to kill his own baby daughter, Oksana Grigorieva, her son -- and even himself --  during the brutal brawl that is being investigated by police, according to statements Oksana has given authorities.

In a stunning world exclusive, RadarOnline.com has obtained all the details of what authorities have been told took place on January 6, the crucial date in the domestic violence investigation against Mel, as well as the custody battle between Mel and Oksana.

EXCLUSIVE PHOTOS: See The First Photos of Mel and Oksana In a Passionate Embrace On The Beach