Microsoft’s latest overture to Yahoo has raised a lot of questions about what exactly it wants from the new round of negotiations. What we do know for sure from the statement it issued Sunday is that Microsoft isn’t currently pursuing an acquisition of all of Yahoo. That leaves all kinds of other possibilities, including joint ventures, partnerships or a deal to acquire just a piece of Yahoo.

Not surprisingly, some tech analysts and bloggers have been working the phones and crunching the numbers to try to guess what such an alternative deal might look like.

Whatever might be in the works, investors generally saw the renewed talks as a modest positive for Yahoo: Its shares were up nearly 1 percent in early afternoon trading Monday.

People involved in the confidential discussions between Microsoft and Yahoo told The New York Times that the latest talks centered on a partnership or joint venture for search-related advertising to compete against Google.

Microsoft, led by Steven Ballmer, clearly wants to head off any collaboration on advertising between Yahoo and Google, the market leader. Yahoo has been racing to complete its own partnership with Google and was expected to announce a formal agreement as early as this week. Microsoft may be trying to persuade Yahoo to shift such a partnership to Microsoft — undoubtedly a weaker ally, but one with fewer potential antitrust problems.

What about the sale of part of Yahoo? Citing speculation from sources at both companies, Kara Swisher, writing on her Boomtown blog, suggested that Microsoft might simply buy Yahoo’s search business and the text-based advertising business outright.

That would allow Yahoo to maintain control of its communication assets, including mail and instant messaging, as well as its many content properties. In that way, Yahoo might be able to keep its identity while outsourcing its ad and search business to Microsoft for a pretty penny.

TechDirt also thinks that Microsoft is gunning for control of Yahoo’s search-related text advertising business, which Yahoo had been considering handing over to Google.

Henry Blodget doesn’t think Microsoft would be smart to buy Yahoo’s search business. Writing on his Silicon Alley Insider blog, he outlines a different kind of combination that he thinks would be better: Microsoft spinning its Internet operations and $10 billion into Yahoo in exchange for 51 percent of the stock.

As for the notion of Microsoft buying Yahoo’s search business outright, which would presumably include Yahoo’s newer Panama platform plus a long-term monetization contract, Mr. Blodget believes that this would be a good deal for Yahoo as he believes that Yahoo’s search business will continue to decline, with or without Panama, so it should get some money for its technology while it can. But he goes on to say that, “at almost any price, however, buying Panama would end up being a lousy deal for Microsoft.”

The analysts at the investment banks have now started to chime in on the discussion. UBS analysts said in a research note that the business discussions between Microsoft and Yahoo could be a prelude to an eventual outright acquisition offer, because it was vital for Microsoft to acquire Yahoo on friendly terms.

“A near-term deal could act as an intermediate step that would go a long way toward testing the waters,” UBS wrote.

TechCrunch believes that Microsoft may just be “toying” with Yahoo as Yahoo tries to finalize their search outsourcing deal with Google this week.

So what happens next? Literally anything, says TechCrunch. Microsoft could partner with Yahoo on a search deal. Or Yahoo may do something with Google instead and fight it on the regulatory front. Or the possibility of a full-scale acquisition may be put back on the table.