Previously private communications between leading figures in the private-equity industry were released to the public Wednesday evening by a federal judge in Boston, revealing the clubby nature of their relationships and the extent to which rival firms cooperated in some of the biggest leveraged buyout deals in history.

“They are very happy campers that we are not going any further,” wrote Henry Kravis, founder of the private-equity firm KKR in an e-mail referring to a conversation he said he had recently with a top executive of a rival firm about an upcoming deal.

To the pension fund and individual plaintiffs in the long-standing case, Dahl v. Bain Capital , such e-mail communications reveal “a conspiracy” in which major firms “would allocate deals among themselves.” The suit alleges each firm “took a turn as the ‘winner,’ ” enabling them to “maintain order while ensuring that they paid the lowest possible prices for companies.”

To the private-equity firms, the newly released e-mails may be titillating, but don’t reveal a conspiracy or anything inappropriate. In fact, industry officials say some cooperation was necessary to make possible the very large and profitable deals — known as “club deals.” They point out that all were accepted by the boards of the companies being acquired.

“The plaintiffs do not challenge the perfectly legitimate practice of club deals,” said Kristi Huller, speaking for KKR. Instead, she said, they “make the preposterous claim that the entire private-equity industry came together under a master plan to decide which firms would be permitted to acquire any particular public company. There is no evidence of such an arrangement, and the facts in the case show exactly the opposite: private-equity firms spending millions of dollars pursuing companies that they never acquired, repeatedly increasing the prices they offered and paying substantial premiums to shareholders through multiple rounds of hotly contested bidding.

In addition to KKR, the defendants include the biggest names in the industry — Washington-based Carlyle Group; Bain Capital, the firm started by Republican presidential nominee Mitt Romney; and the Blackstone Group.

The lawsuit alleges that the firms colluded on 19 deals, including some of the biggest buyouts in history, including the purchase of hospital operator HCA. All of the deals occurred years after Romney left Bain, and he is not mentioned in the suit or the e-mails.

The unabridged complaint gives an inside view of the $33 billion buyout of HCA, at the time in 2006 the biggest private-equity deal ever. The plaintiffs allege that KKR, Bain and Merrill Lynch paid less than market price for the company because other private-equity firms, including Carlyle and Goldman Sachs, agreed not to compete against them. The plaintiffs allege that the lower price cost shareholders more than $1 billion.

The unredacted document shows e-mails from some of the most powerful men in finance agreeing not to bid against KKR and Bain because they didn’t want to harm their relationships with the firms.

In the e-mails, David Rubenstein of Carlyle explained that he didn’t want his firm to bid in part because he wanted to preserve Carlyle’s relationship with KKR.

“Some have proposed we try to compete by participating in a competing deal [HCA],” he wrote, according to the complaint. “I do not think that is a good idea for many reasons, but particularly because I do not want to be in a . . .battle with KKR at the same time we are teaming on other deals elsewhere.” A Carlyle spokesman declined to comment Wednesday.

In another set of messages, TPG Managing Director Jonathan Coslet wrote to his colleague Philippe Costeletos about his firm’s decision, as well, not to bid: “I spoke to both Michaelson [at KKR] and Pagliuca [at Bain] and told them we had decided to pass on the HCA situation.”

Costelatos wrote back: “Probably the right decision even though I hate to see a good deal get away. I guess we’ll find out some day how much our relationship means to them.”

TPG spokesman Owen Blicksilver said: “TPG never colluded to suppress deal prices. We competed vigorously for deals that the firm both won and lost.”

The defendants have filed to have the case effectively dismissed. The judge is expected to rule in coming months.