be (one's) baby(redirected from be their baby)
be (one's) baby
1. To be a project or goal that one has initiated and is very devoted to realizing. That initiative is Cheryl's baby, so you know she's going to do everything she can to make it successful.
2. To be one's cherished possession. That car is Mike's baby. If it gets a scratch, he'll be inconsolable.
be someone's baby
If you say that something is someone's baby, you mean that they have created it or are responsible for it. He's open to ideas for the movie, but it's his baby. There's no doubt Fashion Week is her baby.