If you ask me, the effort by Australian mining giant BHP Billiton (NYSE: BHP) to spend $38.6 billion for Canada's PotashCorp (NYSE: POT) is as dead as a doornail.

When Potash's board reacted with a quick rejection of its opening gambit, BHP "went hostile," appealing directly to the target company's shareholders. Since then, and while the proposed deal has been traveling along the Canadian regulatory road, there have been discussions in a variety of quarters regarding the possibility of a rival bid from China's Sinochem, or from a group of sovereign funds, or even from miners Rio Tinto (NYSE: RTP) or Vale (NYSE: VALE).

It was a requirement of the process that, in order to gain Canadian regulatory approval, BHP needed to demonstrate that its proposed combination would provide a net benefit to Canada. But even after offering a number of concessions during negotiations, the miner clearly wasn't able to accomplish that.

So this week, with the deal strongly opposed by Saskatchewan Premier Brad Wall, along with three of his peers in other provinces and lots of other Canadians, it wasn't particularly surprising when Industry Minister Tony Clement turned thumbs-down on it. BHP officially has 30 days to effect a change of sentiment in Canada, but you clearly can put a fork in the potential for a combination, and the major question now becomes one of where BHP goes next.

Opinions are like navels: Everyone seems to have one. But since you've asked, let's examine mine -- my opinion, that is. First, despite all of its obvious strengths, BHP hasn't had the world's best deal-making record of late. Not long ago, regulators in Asia and Europe quashed its planned iron ore joint venture with Rio Tinto. And in 2008, an outright acquisition of Rio was also dispatched.

Beyond that, however, it seems that there are at least a couple of viable directions available to the company, both of which assume that it will stick with its greenfield Jansen Project potash mine in Saskatchewan. First, it might further assuage its potash pangs -- something it apparently now shares with Vale and Rio -- and make overtures to Mosaic (NYSE: MOS) or Potash One, for starters.

Otherwise, it could choose to expand its copper or aluminum presence by making eyes at the likes of Freeport-McMoRan (NYSE: FCX) or Alcoa (NYSE: AA), something I've thought was a possibility for a while. Regardless of which direction it might select, I'd expect it also to continue its global oil and gas expansion.

BHP may have been rebuffed, but it's hardly out of luck. It remains very much the solid company it was before it showed its wallet off in Canada. On that basis alone, it should remain a favorite of Foolish investors.