Tim keeps tabs on Steph's baby. He tells himself he's doing it for her; that Steph would have wanted to know. (Steph didn't want to know; she'd told him that she would have died a little inside each day, knowing she couldn't be there.)
But Steph is dead, and this little girl is all he has left besides his memories, which still hurt.
It doesn't hurt, what he finds out about Steph's baby. Her new parents, Mr. and Mrs. John Kelly, lost their own daughter to the Clench during No Man's Land. Her name was Carrie. They miss her dearly, they tell the adoption agency, and want another little girl to love.
They name Steph's daughter Mary.
Tim keeps a close eye on them, making sure that grief doesn't drive the Kellys to do something stupid, as it has others. They don't; they're model parents, and shower Mary with all the love and attention any little girl could ever want. (All the love and attention Steph deserved.)
As the years go by, and Mary grows older, his periodic checks on her become more sporadic. What the Joker tried to do to him – no matter that he doesn't remember, thanks to J'onn J'onzz – makes him decide that his original plan to only be Robin temporarily, was a sound one. He's too old to be a Boy Wonder, anyway. He needs to get out, while he still has some of his sanity left.
Mary is Steph with red hair; she can take care of herself.
One day he finds a wedding announcement in the local newspaper; she and her boyfriend of two years, Warren McGinnis, are getting married on the anniversary of Steph's death.
Tim hides his tears in the newsprint, the memories hurting just as much nineteen years later, and hopes this isn't prophetic of years to come.
Warren McGinnis is gunned down seventeen years later, and Tim makes sure Mary and her two boys get the full life insurance payment. There's nothing else he can do for them…now. He has a life of his own, after all, even if it isn't the one he would necessarily have chosen. (Dick is Bruce's son, but he's the one working for Wayne Enterprises.)
Seven months later he sees the new Batman on television. When Dick calls to tell him about Terry, Tim isn't surprised.
No one ever really leaves.