The sale and move of the Thrashers, approved Tuesday by the NHL board of governors, leaves Atlanta with three major-league sports franchises. And while none of the three are in danger of relocation, two have ownership situations that could be conservatively described as, well, fluid.

Here’s a look inside the owner’s box of the Hawks, Braves and Falcons:

The Hawks

The seven-man Atlanta Spirit ownership group hasn’t put a public, unambiguous “for sale” sign on the Hawks, as it did on the Thrashers in mid-February. But through its investment banker, the Spirit has had talks with prospective Hawks purchasers over the past year.

Although part-owner Michael Gearon Jr. has said he wants to retain his stake, the group signaled its willingness to sell a majority interest in the team by entering into an exclusive negotiating agreement this spring with John Moores, the outgoing owner of the San Diego Padres. The exclusivity period ended May 20 by mutual agreement after negotiations built little momentum, but Moores is believed to remain interested.

Like the Thrashers, the Hawks lose money. But while the Spirit pegged the Thrashers’ losses at $20 million per year in court documents, the Hawks are losing about $7 million per year, according to Forbes magazine’s annual study of NBA franchises.

With the more modest basketball losses offset by the profitable Philips Arena, the owners do not feel the same pressure to sell the Hawks as they felt with the Thrashers.

Even if sold, the Hawks are not in danger of following the Thrashers out of town because the bonds that funded the construction of Philips Arena require the team to “play all of [its] regular season and playoff home games” in the arena “for as long as the [bonds] are outstanding.” The bonds are scheduled to be paid off in 2028.

The Braves

When Liberty Media acquired the Braves from Time Warner in 2007, the deal had nothing to do with baseball and everything to do with taxes. It was such an unusual transaction that baseball commissioner Bud Selig insisted on a pledge from Liberty to keep the team for 4 1/2 years — a commitment that expires in a few months.

Here’s the story (abridged version) of how Liberty came to own the Braves, a story that also explains why almost no one expects the company’s ownership to be indefinite:

The Colorado-based conglomerate, led by media mogul John Malone, owned a huge block of Time Warner stock and wanted to sell much of it. Time Warner, in the process of a stock repurchase program at the time, was a willing buyer. But simply selling the stock for cash would have saddled Liberty with hundreds of millions of dollars in capital-gains taxes.

That’s where the Braves came in as a convenient currency.

A provision in the tax code allowed for a tax-free transaction if the stock were exchanged for operating asset(s) as well as cash. So a deal was struck, closing 10 minutes before a change in the tax law: Liberty exchanged 68.5 million shares of its Time Warner stock for the Braves, a group of craft and decorating magazines and, more significantly, $960 million in cash.

Liberty is free to sell the team after this season, but the company hasn’t commented on its intentions. (Of course, Liberty hasn’t commented on anything else about the Braves, either, since buying the team.) On Liberty’s quarterly conference call with investment analysts last month, there was no mention of the Braves. The team is a tiny portion of the company’s holdings, which include home shopping network QVC, movie service Starz and many other businesses. But Liberty did say one of its corporate goals is to “rationalize non-core investments.”

The Falcons

The Falcons are the bastion of stability among Atlanta’s sports franchises, at least at the ownership level.

Arthur Blank is the dean of the city’s sports owners, approaching his 10th season as Falcons owner. He sold small stakes to five investors in 2009, making seven limited partners in all, but has shown no inclination to sell a larger stake.

Blank attempted to buy the Braves in 2006. His Falcons currently have plenty on their plate business-wise: the NFL lockout and the team’s desire for a new open-air stadium downtown.