There is a nursery, and all babies go there for monitoring and some routine tests after being born, but most of the time the baby is in the room with the parents. Both parents get plastic wristbands and the baby gets them in two spots, and a monitor. The ONLY way that you can take a baby out of the maternity ward without causing an emergency lockdown of the hospital is to arrive with an infant car seat (even in places like NYC where some people can walk home), show your wristband, see that it matches the baby's, have them remove the monitor and walk you out of the hospital with your baby in the car seat.