You know that old saying, about there being no second acts in American Life? Don't tell that to PayPal, whose eBay parent announced today that it's spinning off the payments company by mid 2015.

PayPal's new independence is at least the third act for PayPal, which was founded by tech luminaries Elon Musk, Max Levchin, and Peter Thiel in the late 1990s. PayPal first rose to prominence as the defacto standard to pay for things on the Web before secure, online credit card transactions were widespread. It was then acquired by online marketplace eBay in 2002, for whose merchants it has served as a primary financing mechanism for sales.

In freeing itself from eBay, PayPal will have the mobility it needs to face competitive challenges from the likes of Apple Pay and Alipay, the payments subsidiary of the newly public Alibaba. But it may also be able to get back to its entrepreneurial roots, and develop new lines of business not specifically tied to its former parent.

"PayPal has fallen flat in mobile [payments] and perhaps now they can focus on a competitive strategy to capture a larger part of the mobile payments market," says Nathalie Reinelt, an analyst with Aite Group.

In recent years, PayPal has tried to tackle a growing consumer and business demand for payment options by allying itself with companies such as Home Depot, which allow customers to pay at the cash register using their PayPal accounts. PayPal has also ventured of late into business finance through its working capital loans

Free of eBay, PayPal could now pursue a public offering, or even a banking license, says Brian Riley, senior research director for CEB TowerGroup.

And a public offering "would be good timing, with Alibaba's IPO and Apple hitting the market with a lot of flash," Riley says.

More specifically, Apple's newly released iPhone 6 has an embedded chip in it that securely encrypts mobile transactions, giving new life to the concept of a digital wallet, which had languished for years.

PayPal could potentially do for Android phones what Apple is doing for its own operating system with payments, says Reinelt. "There is a huge opportunity for a company to mirror Apple's mobile payments approach for the other half of the smartphone population," Reinelt says, adding that PayPal could begin developing similar chip-based payments technology using the cloud for verification and security.

A newly indpendent PayPal could also allow it to be more nimble to tackle a potential competitive threat from Alipay, the payments company owned by Jack Ma, whose Alibaba went public less than two weeks ago. Much the way PayPal allows eBay merchants to accept payments, Alipay serves as the payments conduit for Alibaba. 

Alipay, however, dwarfs PayPal. It has about 300 million users who conducted about half a trillion dollars in transactions in 2013,  according to some estimates. PayPal's user base is about half of Alipay's, and in 2013 conducted about $200 billion worth of transactions.

Nevertheless, PayPal has international aspirations. It currently does business in 203 markets, and in 26 different currencies, and it has a strong international money transfer business, Reinelt and Riley say.

"It's a natural evolution for Paypal, and now they won't be so dependent on eBay," Riley says.