By the time he died Oberyon had 19 kids by 9 women, and his daughters were married off to a host of high borne lords. Renly, Joffrey Baratheon (the son of Stannis weirdly), Loras Tyrell, Edmure Tully.
His second surviving son (pneumonia claimed like 5 of my children) married the heir to the Iron Throne, Robert insists on attempting to outlive everyone, with Ned Stark, Jon Arryn, Mace Tyrell, Doran Martell, Hoster Tully and Tywin Lannister all dead.
My heir Tristifer looks set to follow in my footsteps, having fathered 6 children by 5 women, including the current Lord Paramount of the North, a daughter of Ned Stark. Robb joined the Kingsguard and holds Ice, Jon Snow was never legitimised and married a daughter of mine and holds a fief in the North.
Jon Arryn's daughter died aged 14, meaning the Vale reverted to King Robert, although Renly would usurp it, making him a dual Lord Paramount, to the disgust of several local lords who rebelled. Renly dies, my granddaughter becomes Lady Paramount of the Stormlands and the Vale, although another rebellion occurs.
Robert's now known as 'the Unworthy' and for the first time in a game Cersei still lives. She usually dies of gonorrea.