WASHINGTON — In court documents that lawyers for Bain Capital sought to keep secret, the company and other leading private equity firms are depicted as unofficial partners in a bid-rigging conspiracy aimed at holding down the prices of businesses they were seeking to buy.

In Bain’s biggest acquisition, the $32.1 billion purchase of hospital giant HCA in 2006, competitors agreed privately to ‘‘stand down’’ and not bid on the company as part of an understanding with Bain to divvy up companies targeted for leveraged buyouts, according to internal e-mails.

The documents have become part of a lawsuit in US District Court in Boston brought against Bain and other firms by shareholders who say the firms’ bid-rigging artificially deflated the sales price of more than two dozen companies and cost them billions of dollars.

Bain, founded by Republican presidential nominee Mitt Romney, is a defendant in the lawsuit, which also names Goldman Sachs’ private equity arm and the Blackstone Group, the firm run by the investor Stephen A. Schwarzman.

The corporate takeovers at issue in the lawsuit include the acquisition of prominent companies like Neiman Marcus, Toys R Us, Michaels Stores, Univision, and the Loews and AMC movie chains, and they date from 2003 to 2007. The class-action shareholders’ lawsuit, which was filed in 2007, has grown since then after a series of court rulings.

Romney is not mentioned in the publicly released portion of the documents, and lawyers for Bain said in opposing the Times’ motion to unseal the entire filing that he ‘‘could not have been involved in the deals at issue here’’ because he had already left Bain by the time the first deal was finalized.

Lawyers representing the private equity firms have rejected the allegations. In an earlier filing in the case, they said that the lawsuit merely described routine dealmaking tactics and labels them anticompetitive.

And while the firms’ lawyers acknowledge that there are some embarrassing e-mails still under seal, they say that their clients want to keep the court filings private primarily to avoid disclosing confidential competitive information. Private equity executives also reject the idea that they colluded to drive down the prices of their acquisitions.

“These shareholders should be grateful that we purchased their companies when we did, right before the financial crisis hit,’’ said a senior buyout executive who spoke on the condition of anonymity because of the litigation.