We're all familiar with the classic tip of pouring a few drops of vinegar into the water then giving it a swirl before adding your eggs for poaching.
Of course, Julia Child had a better way: hard boil an egg for 10 seconds before cracking it into the water.
First, poke the large end of an egg with a pin to release any air that might cause the egg to crack, and then lower it into boiling water and let it stay for exactly 10 seconds. Lift the egg from the boiling water with a slotted spoon and allow to cool before handling.
After the egg cools enough to handle, crack and gently drop into the poaching water. The lightly boiled egg should have a better chance of holding together after the 10-second boil.