The Red Hood - Sole Survivor

Prelude - The Aftermath

There was no funeral. Officially, Bruce Wayne was just missing - tabloids speculated that he fled his public life for something quieter, or he'd been abducted by some secretive elitist cult in Gotham's underbelly. Unofficially, known only to the members of the family, Batman had been dead for over a month - Killed when the watchtower fell back into the earths atmosphere following an attack from the earths less friendly governments taking a harsher stance on the Justice League in recent years and while the rest of the members survived thanks to his sacrifice, the league broke up shortly afterwards. Richard retrieved the body from the wreckage and had brought it back to the manor, Alfred had insisted Bruce's death be kept secret so he was laid to rest in the Batcave itself, under the computer specifically - the Batcave now being a memorial to Batman. 

After his death, the family took some time to decide among themselves what to do. Richard naturally took up the mantle and leadership position within the family , knowing if they were to hide what had happened batman couldn't simply disappear. Him, Tim and Barbra stayed at the Batcave and Wayne manor with Alfred with Tim staying on as Robin although working far less closely with Richard as he had with Bruce and Barbra, still restricted to a wheelchair, stayed on as their Oracle now working from the Batcave itself. Damien also stayed in the beginning however he was slowly estranged from the family and one day he returned to life with Talia and the League of Assassins. 

As per usual; Jason was different. Jason , being the dramatic person he was, felt as though he should have been the one to die rather than Bruce and this mentality spiraled into huge disagreements with the rest of the family. While Richard had simply decided to keep going with Bruce's ideology, Jason couldn't. He blamed Bruce's death , partly, on that ideology - The fact that heroes seemingly had little impact on crime but had almost unchecked power was the political issue that had lead to the attack and Jason's conclusion was that this was because most heroes where too lenient in allowing the worst of criminals to continue breathing.  Jason's conclusion wasn't a new one for him , he'd been killing criminals even under Bruce as the Red Hood however now without Bruce to hold him to some kind of  ramification , this ideology had devolved from killing the worst of the worst , slowly but surely, into killing the majority of criminals. After weeks of conflicts with Richard, Jason eventually left and took over the old clock tower as his own little Batcave - cutting it off from the rest of the families systems  , he went totally solo now operating almost totally outside of the law and almost totally alone.