Hollywood leading lady GWYNETH PALTROW is waging a war against the paparazzi because she is determined to ensure her daughter APPLE's safety. The SHAKESPEARE IN LOVE actress and her rocker husband CHRIS MARTIN moved from their luxurious London town house to a New York City apartment in a bid to keep tabloid photographers at bay. And Paltrow doesn't stop there - she keeps a log of every run-in she has with photographers in case their behaviour gets out of hand and she needs to involve the police. She tells PageSix.com, "If I have my daughter in the car and they are making me nervous, I'll do whatever I have to do. "I keep a whole log. I take pictures of their cars, write down license plate numbers, everything. If they do it again, I can go to the police. I know my rights, and believe me, I will have them arrested. I will stop at nothing."