The past weekend in baseball offered the latest evidence of the extraordinary rise in the price of sports TV rights and their growing impact on the field and onscreen.

The Los Angeles Dodgers, bankrupt less than a year ago under former owner Frank McCourt, completed a historic trade with the Boston Red Sox on Saturday, instantly taking on more than $250 million in salary commitments — with little more than a shrug and a smile, gestures for which they could thank the TV industry.

While some wags took Dodger ownership’s carefree attitude as a sign of business insanity, others saw simple confidence in the lucrative local cable rights deal the Dodgers are negotiating.

Fox, which holds the Dodger cable rights through the end of the 2013 season, has an exclusive negotiating window for an extension with the franchise through Nov. 30, along with a right of first refusal after that date. While Fox declined Monday to comment on current talks, all indications are that the communications lines between the current partners are open.

Given what the Dodgers’ demands now figure to be, there’s little sign that the current sports rights bubble — which most recently funded a reported $3 billion, 20-year deal last winter for the Los Angeles Angels — is about to pop.

Estimates for the Dodgers’ TV extension start at $4 billion over 20 years, though that amount could be altered depending on whether the baseball team takes equity in the television business. Interest in the Dodgers could be fueled by their aggressive player moves, including Saturday’s acquisition of slugging first baseman Adrian Gonzalez, among others.

In addition, the team’s biggest TV celebrity of all, Vin Scully, announced Sunday that he would return in 2013 for his 64th season behind the Dodger mic.

The Guggenheim Baseball Management group, which acquired the Dodgers for an unprecedented $2.15 billion in March, may delight in opening a bidding war between Fox and such competitors as Time Warner Cable, which would welcome the Dodgers as a compliment on its soon-to-launch Los Angeles Lakers channels — but Fox would logically think long and hard before letting things get that far.

The twist is that viewership for Dodger broadcasts, though it has increased approximately 60% from the McCourt doldrums of 2011, is at 105,000 households per game, meaning that ad revenue is not exactly the stuff of billions. For the broadcaster, analysts say that the key to making the soaring payouts work is mining the exclusivity that accompanies them, with monetizing opportunities in cable and satellite carriage fees, for example.