Of the four poached eggs in my eggs florentine, only one emerged from the pan with a white neatly surrounding the yolk -- and it was not the one I had dropped into the centre of the whirling water first. I watched with envy recently as my brother-in-law prepared a perfect specimen. As with rice, you either have the knack or you do not. But appearance is not everything.
The theory is that you bring the water to the boil, stir it, and drop your egg into the centre of the whirlpool, encouraging the white to cohere round the yolk. I suspect that if it is going to cohere, it will do so no matter what you do; and if it is not, it will not.
Turn down the heat to the lowest simmer, so that the whites do not toughen. Some people think that salt in the water toughens the whites; in fact, it helps to keep them soft, as does vinegar.
Poached eggs take longer to set than the books advise, in my experience. Perhaps that is because I do not like runny yolks. Four to five minutes is about right.
I transfer the eggs to a wooden board to drain for a few moments. Not infrequently, I break one of the yolks when I lift them up again.