RTSE3QA.jpg Lifestyle & Belief A few British companies are moving from paternity/maternity leave to the next frontier: 'Paw-ternity.' PRI's The World April 28, 2016 Paw-ternity leave. Did you catch that? "Paw"-ternity leave. Some companies in the UK are trying out the idea of giving their employees paid time off when they adopt a new pet.