White vinegar is indeed the solution. And don't boil them. Simmer them.

Old eggs have runny whites so use fresh eggs. I also like to use a spoon of vinegar to help keep the whites together.

Doesn't a teeny bit of white vinegar in the boiling water help to keep the white from running??

Get the water simmering then slowley get it swirling with a spoon - pre-crack the egg into a little dish and gently drop it in, the swirling motion of the water will help to gather the white and keep it from going all over the place