Actress Brooke Shields has a pretty impressive pedigree — hanging from her family tree are Catherine de Medici and Lucrezia Borgia, Charlemagne and El Cid, William the Conquerer and King Harold, vanquished by William at the Battle of Hastings.

Shields also descends from five popes, a whole mess of early New England settlers and the royal houses of virtually every European country. She counts Renaissance pundit Niccolo Machiavelli and conquistador Hernando Cortes as ancestors.

What is it about Brooke? Well, nothing — at least genealogically.

Even without a documented connection to a notable forebear, experts say the odds are virtually 100 percent that every person on Earth is descended from one royal personage or another.

"Millions of people have provable descents from medieval monarchs," said Mark Humphrys, a genealogy enthusiast and professor of computer science at Dublin City University in Ireland. "The number of people with unprovable descents must be massive."

By the same token, for every king in a person's family tree, there are thousands and thousands of nobodies whose births, deaths and lives went completely unrecorded by history.

We'll never know about them, because until recently vital records were a rarity for all but the noble classes.

It works the other way, too. Anybody who had children more than a few hundred years ago is likely to have millions of descendants today, and quite a few famous ones.

Take King Edward III, who ruled England during the 14th century and had nine children who survived to adulthood.

Among his documented descendants are presidents (George Washington, Thomas Jefferson, John Quincy Adams, Zachary Taylor, both Roosevelts), authors (Jane Austen, Lord Byron, Alfred Lord Tennyson, Elizabeth Barrett Browning), generals (Robert E. Lee), scientists (Charles Darwin) and actors (Humphrey Bogart, Audrey Hepburn, Brooke Shields).

Some experts estimate that 80 percent of England's present population descends from Edward III.

A slight twist of fate could have prevented the existence of all of them.

In 1312 the close adviser and probable lover of Edward II, Piers Gaveston, was murdered by a group of barons frustrated with their king's ineffectual rule. The next year the beleaguered king produced the son who became Edward III.

Had Edward II been killed along with Gaveston in 1312 — a definite possibility at the time — Edward III would never have been born. He wouldn't have produced the lines of descent that ultimately branched out to include all those presidents, writers and Hollywood stars — not to mention everybody else.

Of course, the only reason we're talking about Edward III is that history remembers him. For every medieval monarch, there are countless long-dead nobodies whose intrigues, peccadilloes and luck have steered the course of history simply by determining where, when and with whom they reproduced.

The longer ago somebody lived, the more descendants a person is likely to have today. Humphrys estimates that Muhammad, the founder of Islam, appears on the family tree of every person in the Western world.

Some people have actually tried to establish a documented line between Muhammad, who was born in the 6th century, and the medieval English monarchs, and thus to most if not all people of European descent.

Nobody has succeeded yet, but one proposed lineage comes close. Though it runs through several strongly suspicious individuals, the line illustrates how lines of descent can wander down through the centuries, connecting famous figures of the past to most of the people living today.

The proposed genealogy runs through Muhammad's daughter Fatima. Her husband Ali, also a cousin of Muhammad, is considered by Shiite Muslims the legitimate heir to leadership of Islam.

Ali and Fatima had a son, al-Hasan, who died in 670. About three centuries later, his ninth great-grandson, Ismail, carried the line to Europe when he became Imam of Seville.

Many genealogists dispute the connection between al-Hasan and Ismail, claiming that it includes fictional characters specifically invented by medieval genealogists trying to link the Abbadid dynasty, founded by Ismail's son, to Muhammad.

The Abbadid dynasty was celebrated for making Seville a great cultural center at a time when most of Europe was mired in the Dark Ages. The last emir in that dynasty was supposed to have had a daughter named Zaida, who is said to have changed her name to Isabel upon converting to Christianity and marrying Alfonso VI, king of Castile and Leon.

Yet there is no good evidence demonstrating that Isabel, who bore one son by Alfonso VI, is the same person as Zaida. So the line between Muhammad and the English monarchs probably breaks again at this point.

But if you give the Zaida/Isabel story the benefit of the doubt too, the line eventually leads to Isabel's fifth great-granddaughter Maria de Padilla (though it does encounter yet another potentially fictional character in the process).

Maria married another king of Castile and Leon, Peter the Cruel. Their great-great-granddaughter was Queen Isabel, who funded the voyages of Christopher Columbus. Her daughter Juana married a Hapsburg, and eventually gave rise to a Medici, a Bourbon and long line of Italian princes and dukes, spreading the Mohammedan line of descent all over Europe.

Finally, 43 generations from Mohammed, you reach an Italian princess named Marina Torlonia.

Her granddaughter is Brooke Shields.