Hah. Tim totally contemplated kidnapping the baby all for himself after Steph died. Then he realised he'd have to explain why he'd come home with a toddler to Jack. The impulse returned, many times, until Tim found a way to visit Stephling without letting anyone know who he was. He probably volunteers at the kindergarten or something.
I'm not sure if Bruce knew or he figured it out. Maybe Bruce tracked Stephling down after Steph's death, out of guilt, and then went to program the computer to keep an eye on Stephling... and found the programming already there.