Ballhawks go to games with the intention of grabbing any ball that goes in the stands, especially milestone home runs like a player's first or 500th. Most then refuse to give them back to the player unless he coughs up something valuable in return, from a signed bat or a jersey to up to $10,000. This breed of sophisticated collector now appears more determined than ever, stalking everyone from rookies like Mr. Coghlan to veteran stars such as Ken Griffey Jr.