The secret to making the perfect poached eggs that hold together when placed in the water is using the freshest eggs possible. The white clings more strongly to the yolk and the yolk is less likely to break the fresher the eggs are.
So, break the cold eggs into a small dish and add them slowly to simmering water (with one tablespoon of white vinegar in it). As soon as the outsides of the eggs begin to set, lower the heat to just barely a simmer. Remove with a slotted spoon and enjoy!