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Actress January Jones recently announced that she was pregnant with her first child last week.

Unlike most celebs, however, she refused to name the baby's father, and said through her rep that she intends to be a single mother.

But while her decision is unusual, she's not alone.

HOT SHOTS: January Jones.

Last year “Top Chef” host Padma Lakshmi didn’t announce the father of her first child either.  Ina a subsequent custody battle, the father was revealed to be Adam Dell, brother of computing giant Michael Dell.

Movie star Minnie Driver gave birth almost three years ago, and did not publicly divulge the father’s identity. Former “Spice Girl” Geri Halliwell also stayed mum regarding her baby daddy when she fell pregnant in 2006.

So while the celebs' secrecy likely stems from privacy issues, does it do anything to the fathers' custody rights?

“The fathers of their children have an equal right to custody...if they wish to exercise that right.  The flip side of that is that if they're not married, those men would be obligated to provide child support until the child is 18,” explained California attorney, David E. Wohl. “(The father is often not named) also due to legal issues such as child support, legal and physical custody, and while visitation rights are being negotiated. Those negotiations can be lengthy and sometimes one of the issues is the confidentiality of the father's identity – especially if the father is married to someone else.”

Even if the paternity is not named on the birth certificate, Wohl said the father has a limited time to come forward.

“If the father is not named on the birth certificate and they believe they are the legal or biological father they will generally have two years, or in some states three years, after the child is born to demand a paternity test,” he said. “If no father is named and no one steps forward to assert paternity then the child will have no legal dad. Another reality is that the mom simply may not know who the father is, and she may be embarrassed to admit that! If she's a self sufficient wealthy star, the child could be well cared for in any event.”

Even if she wants to, how long can a star in the spotlight keep the father of their child nameless? After all, Lakshmi’s well-kept secret was exposed when Dell sued her for custody in January – but had he never taken legal steps, his identity could have potentially been hidden forever.

According to Wohl, if she can keep her mouth shut, and the father is not pursuing custody, the answer is : forever.

“A mom is not legally required to name the father of her child," Wohl said. "Even if she applies for public assistance she will not be forced to name a father.”