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In Final Crisis, Bruce as Batman is hit by Darkseid's Omega sanction which sends his conciousness to a parallel universe. This leaves the charred body in the cowl that Superman discovers, but the arc ends with Bruce being present much earlier in time, and watching Anthro die, and lying his utility belt on Anthro's corpse before inscribing the bat symbol on the cave wall.

Following the events of Final Crisis, the Superhero community and Batman family mourn the loss of Bruce as covered in the lead up to and "Battle of the Cowl" series. Dick Grayson is initially against taking on the cowl, and retains his Nightwing Persona. As the villains of Gotham become more bold, another anti-hero claiming to be Batman starts dishing out his form of justice, but is much more violent, and resorts to killing people and using guns. This causes a rift between Tim (Robin #3) and Dick (Robin #1), with Tim insisting that Gotham needs a real Batman, and Dick refusing to step up. Eventually, it is Tim that dons the Cowl and becomes Batman to take down the Violent Batman, but is badly wounded in the ensuing battle. Dick, as Nightwing, having worked out that the violent Batman alter-ego is none other than Jason Todd (Robin #2/The Red Hood/Red Robin) goes and does battle with him, eventually defeating him when Jason falls from a bridge into the River. The badly wounded Tim is rescued by Damian Wayne (Son of Bruce and Talia Al Ghul).

Following the events of this arc, Dick realises that Gotham needs a Batman, and that Bruce is really gone. He steps up, and takes on the mantle of the bat, becoming the Batman, and taking on Damian Wayne as his Robin, refusing to allow Tim to continue as Robin as he sees Tim as an equal, while Damian is his subordinate. This further alienates Tim, and he abandons the mantle of Robin, but takes on the guise of Red Robin, theorising that that costume is already tainted, meaning that he can bend the rules in it.

As the DCU sits at the moment, Dick Grayson is Batman and Damian Wayne is Robin as both protect Gotham. Tim is using the Red Robin costume to travel the world in search of Bruce, who he believes is still alive. Terry McGinnis is yet to enter the current comic continuity, and although he has made appearances, he is not considered to be Batman JUST yet.

Final Crisis 6.

Technically Batman is not dead his consciousness was sent to a Parallel world by Darkseids "Omega Sanction"

in final crisis, darkseid kills him

terry hasn't been "introduced" into the comics yet, if ever. it's dick grayson

He got kicked out of a Helicopter by his father, Dr Wayne.