Becca Robb was the pregnant young woman who was going to give up her baby for adoption to Lisa Cuddy in the Season 5 episode Joy.

Becca first meets Cuddy in a coffee shop and tells her that she picked Cuddy because she was impressed about how responsible her job was.  Becca explains she was a heroin addict, but gave it up when she found out she was pregnant.  However, Cuddy notices Becca has a rash on her arms and takes her to the hospital.  

Cuddy is very worried, but Allison Cameron runs tests and can find nothing wrong.  Cuddy still orders more tests and admits Becca.  An ultrasound eventually reveals that the fetus's lungs are underdeveloped.

Becca takes a turn for the worse when she suffers a placental abruption.  Cuddy orders a transfusion, but realizes allowing the baby to come to full term puts Becca at risk.  Cuddy seeks advice from House, but he realizes she is just looking for permission to delay delivery.  Cuddy asks Becca to accept treatment and wait, but Becca is afraid of dying and asks that they deliver the baby immediately.

They perform a cesarean section and deliver the baby.  At first, it can't breathe, but at Cuddy's urging it finally draws a breath and starts crying.  

However, after the experience, Becca realizes that despite the disadvantages she and the baby face, she wants to raise the baby herself and not put it up for adoption.

Character page at IMDB

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