...well, first off, one shouldn't boil the egg, at least to Hervé This (pronounced Tees), one of the group of people involved in molecular gastronomy. Molecular gastronomy is the application of science to the making of food.

When approaching cooking as science, perfection can be qualified. So what does a perfect hard boiled look like? When you cut the egg open, the hardened yolk should be centered. The egg yolk should not have the green sulfur on the cooked outside. And the whites, when cooked, should be soft and tender. But how to get to that state of perfection?

The idea is to cook the eggs slowly. As This notes in his book, "Molecular Gastronomy - Exploring the Science of Flavor":

How do eggs cook in the first place? The white consists of about 10% proteins (amino acid chains folded upon themselves in the shape of a ball) and 90% water. During cooking the proteins partially unfold (They are said to be "denatured") and bind with each other, forming a lattice that traps water - in other words, a gel.

The tenderness of the cooked egg white depends on the quantity of water trapped (the loss of a part of this water is what makes overcooked fried eggs rubbery and overcooked egg yolks sandy) and on the number of proteins making up its lattices (more lattices mean that more water is trapped, rigidifying the entire system)...

...When an egg is cooked in boiling water, at a temperature of 100° C (212°F), not only does its mass progressively diminish as water is eliminated from the gell that forms, but many kinds of protein coagulate as well.

By cooking the eggs at a temperature of 154° F (68° C), water loss of the egg is prevented. As long as there is no water loss

As for keeping the cooked yolk in the center of the egg? Prevent it from rising within the shell by rolling it continually.

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