Break the egg into a plastic strainer with a fine mesh first and shake it gently over a bowl. The watery bits of the egg white drain away, leaving the thicker, more glutinous central part of the white. (The watery bit is what streams away in the pan of water and makes a mess.) Then poach eggs as normal by sliding into a pan of simmering water with a touch of vinegar added to it. Makes a tremendous difference if you do the straining thing, to get an egg that is a good shape and holds together well. (A "chef's tip" I read online some time ago, along with "use the freshest eggs possible, at room temperature".)