It's a dog-eat-dog world -- and the legendary Papaya King hot dog stand plans to take full advantage.

Papaya King, which serves franks and its own patented tropical fruit shakes, plans to open a new location in the heart of the freshly scrubbed Times Square this week, on 43rd Street right off of 7th Avenue, The Post has learned.

But that's just the beginning. Over the next 12 to 18 months, Papaya King will be expanding in Manhattan, The Bronx, Brooklyn and college towns in New Jersey and Connecticut with as many as 10 more stores, according to Dan Horan, CEO of PK Operations Inc., which operates the Papaya King brand.

"We are in a period of expansion," Horan told The Post. "Times Square is the perfect place for us to establish our mark. There's no other place in this neighborhood to get a hot dog and our exclusive tropical fruit drinks."

The store windows had been covered until yesterday, when it was first made clear to the public that a new Papaya King was coming. And many of the passers-by couldn't wait - even though a sign said the grand opening wouldn't take place until today.

"They were already trying to get in, and I wish we were ready," Horan said.

The last-minute glitches that were delaying the store opening - a juice machine that didn't fit in the space it was allotted and no electricity - should be cleared up soon.

"We hope it will be as early as tomorrow, or perhaps Monday at the latest," Horan said yesterday.

It's the first extension of the Papaya King brand south of 96th Street in 69 years.

Papaya King first began in the 1930's, with one stand at the corner of Third Avenue and 86th Street. It soon faced an onslaught of competition from similarly named companies like Gray's Papaya or Papaya Kingdom, which set up hot dog and fruit juice stands all over the city.

In 1997, a group of investors decided to buy the rights, titles, interests, propriety recipes, name and logo of Papaya King from the owner of the Upper East Side store, Peter Poulos, the son of the original founder. While he retained the right to continue to run his operation as is, Poulos otherwise let goof the Papaya King brand to PK Operations, where he is a part owner and a member of the board of directors.

PK Operations opened its first Papaya King store last summer, on Harlem's famed 125th Street. The Times Square store will be its second, and the pricing will be the same as in the Upper East Side and Harlem stores.

In other words, two dogs and a drink will cost you $3.99.

Meanwhile, PK Operations is scouting out other prime locations. But the search has not been without its difficulties.

"The red-hot real estate market has made finding good locations tough," admitted Horan, who was hired away from Gourmet Garage last year to head the Papaya King expansion.

To nab the great Times Square space, Horan promised the landlord - a nonprofit organization that trains mentally disabled people who may otherwise be left out of the workforce - to hire two of its trainees as clerks for the new store.