He obviously won't have turn out like he did in Batman TAS.
I think he will continue to be a hero of his own shaping while heavily influenced by Batman. My hope is eventually he changes his identity away from Red Robin. I feel like Robin is batman's young side kick. As Tim grows older, and Batman becomes less of a mentor he should drop the Robin completely as Dick Grayson did.
That said, if Bruce were to retire/be killed, I think Tim is best suited to take the mantle in the future.