Amazon.com Inc will start managing subscription payments for start-ups and other companies – the latest in a series of quiet moves the e-commerce giant has made into PayPal’s turf over the past year. Amazon then charges a fee on each transaction. EBay Inc’s PayPal has long dominated online payments services but Amazon sees plenty of scope to push into new areas. The new service broadens Amazon’s profitable role as a middleman for third-party sellers, which account for 40 percent of its sales and extends its influence beyond its website.