How to have poached eggs in "sphere form"?

The number one thing is having fresh eggs. Older eggs have a looser inner white and there's not much you can do to keep the yolk from hanging on to the side. Contrary to the other answer, I have not found that swirling the water helps the egg stay together, compared to dropping it in very carefully (the water should go into the cup before the egg comes out; you shouldn't be pouring it in, as much as allowing it to slowly slide along the side of the cup further down into the water). The water should be well-salted, and a bit of vinegar can be a good idea although adding too much can cause the outer skin of the egg to become a bit leathery.

If you want a truly absurdly perfect poached egg, you can use a sous vide cooker (or just a pot of carefully tended warm water). Cook the eggs in their shells at 64 degrees celsius for 1 hour, remove the shell and separate the loose white, and cook in simmering water for just a minute or so. I actually find the result a bit off-putting in its perfection, but it's the closest to "sphere form" you will ever get.

Jamie Oliver has a method (around 2:53 in the video) that involves poaching the eggs wrapped in plastic. I've never tried this myself, but the gist from the video is:

1. Tear off a roughly square piece of plastic wrap
2. Line a bowl with it
3. Lightly oil the plastic
4. Crack the egg into the bowl
5. Pull the corners of the plastic wrap together and gently twist it shut, until there's pretty much no air remaining
6. Poach the egg
7. Carefully slice the twisted part off with a knife, then place the egg on whatever you're serving it on and gently slip the plastic off

He insists on fresh eggs as well.

You could try the "Arzak" egg, made popular by Spanish chef Juan Mari Arzak. It is not difficult, but does require the extra step of wrapping. Line a ramekin with plastic wrap, leaving enough overhand to enclose an egg with extra to tie off. Brush with oil. Crack egg into plastic lined ramekin. Carefully bring the plastic end together, encasing the egg, and tie off with a piece of butcher twine, or the plastic wrap itself. Lower into simmering water. Alternately, use string to tie to a wooden spoon that is rested across the pot, so that the egg bundles hand below the surface of the water, but above the surface of the pot. Cook for 5 to 8 minutes, depending on your preferred level of doneness. Remove from pot, unwrap, and serve...or, chill in ice bath for later reheating.

Do the trick of swirling the water first at the moment you will add the egg, remember the water must be boiling, and then add egg by egg in the center of the pot, do not add them all (i meaning to cook more than 2 eggs at once), by doing this it will get the "sphere" form, and cook by the time that you like poached eggs to be.

That's a tall order.

Just to get the coveted "teardrop" shape on a poached egg is hard enough.

Some chefs use scissors to clean up poached eggs to get this shape. A bit of a hack, but maybe you could do the same, and cut it into a spherical shape.

Personally, I tend to get the classic egg-drop-soup shape of my poached eggs.

Although I agree with all the answers already posted, I thought I'd add my approach as I'm pretty proud of how mine come out!

1. Bring a pan to the boil
2. Add around 1-2 tbsp of white vinegar to the water for a medium size pan (more than you might think!)
3. Crack egg into a small flour-sieve (note everything previously stated about the freshness of the eggs)
4. Let any 'loose' white drain off slightly
5. Transfer from sieve into a small ramekin or bowl
6. Turn the water down until it's just on the point of simmering. i.e. there should be very little movement but just a degree or two higher and it would simmer
7. Lower the egg gently into the water (out of the bowl)
8. Leave until the white is just firm, you can test by lifting out with a spoon and poking the bit of the white next to yolk is firm but the yoke is still soft
9. Use a slotted spoon to transfer onto a clean dry piece of kitchen towel before transferring onto toast

Just a note, I used to be a French Chalet chef and would have to cook ~20 eggs every morning so I do not swirl the water to allow me to cook more in one pan at a time. I can't comment on whether this helps or not.