Kate Middleton Carrying Twins?

When Prince William and Kate's official announcement that she is pregnant came Monday, the palace said she was "expecting a baby."

But in light of the fact that the Duchess of Cambridge is also suffering from hyperemesis gravidarum, a form of acute morning sickness, there has been growing speculation that she may, in fact, be expecting twins.

According to the National Institutes of Health, the Duchess's rare condition tends to appear more often in women carrying twins.

So what would it mean for the royal family if Kate, 30 – who was discharged from the hospital Thursday – were to deliver two little royals? A pair of heirs?

Nope, royal experts tell PEOPLE. In fact, it's all a bit complicated.

The firstborn twin would have a completely different path than his or her sibling, says royal historian Robert Lacey, author of The Queen: A Life in Brief: "The first child to appear will have precedence. Whichever one comes out first will be the heir – and it will be the call of the obstetrician if there is a caesarean section."

And the obstetrician will make that delivery based on the location of the babies during labor, Mark Johnson, Professor of Obstetrics at Chelsea and Westminster Hospital, tells PEOPLE.

Says Johnson: "If delivering vaginally, the first baby to enter the pelvis will be delivered first. If delivering by c-section it very much depends on the which baby is closest to the incision, generally that will be the lower of the two babies."

A year ago, the British government voted to modernize the rule of succession so that in the event of twins, a firstborn girl would not lose the title of heir if a boy were to be subsequently born to the royal couple. But that rule hasn't been implemented yet.

Under the current law of the land, says Lacey, "If the twins are a girl first followed by a boy, the boy will be next in succession."

When or if the law is changed, adds Lacey, "the boy would be ousted by his sister."

If Kate is pregnant with twins, William, who will surely be present for the births, will be able to see firsthand which baby is born first. But in the past that wasn't the case, adds Lacey.

In other eras, "the Home Secretary was on hand in the hospital to ensure there was no foul play," says Lacey, "since there were fears that if the firstborn turned out to be a girl, she might get swapped for a substitute baby boy – and smuggled into the bed in a warming pan."