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Mark Zuckerberg likes his privacy, but he’s in an increasingly public battle with a would-be neighbor in Palo Alto, Calif., that threatens to expose details of his personal life and conduct.

New court documents were filed on Wednesday in a continuing lawsuit against Mr. Zuckerberg, the Facebook co-founder and chief executive, revealing a dispute that touches on various hot buttons of boom-time Silicon Valley: privacy, networking, precious real estate, and the pairing of youth and affluence.

In one sworn document, a real estate broker for the man suing Mr. Zuckerberg testified that Mr. Zuckerberg’s own real estate broker referred to him as “just a kid.”

It appears to be the kind of gloves-off tenor characterizing the dispute. One of the documents asks the court for permission to get details about Mr. Zuckerberg’s personal finances and net worth, creating yet another potential opening in the walls Mr. Zuckerberg has sought to build around his private life.

Lawyers for Mr. Zuckerberg have said in court documents that the suit involves aggressive tactics aimed at leveraging a settlement and that the would-be neighbor is “going out of his way to embarrass Mr. Zuckerberg and pressure those around him at every turn.”

Separately, Mr. Zuckerberg was deposed for the case in law offices in San Jose, Calif., for part of the morning and much of the afternoon. A spokeswoman for Facebook said the company does not, as a matter of policy, comment on Mr. Zuckerberg’s personal affairs. But Patrick Gunn, a lawyer for Mr. Zuckerberg, said “the claims asserted in the lawsuit have no merit and my client intends to defend them vigorously.”

As described in the lawsuit, in 2012 a part-time local developer named Mircea Voskerician went under contract to spend $4.8 million to buy a house adjoining Mr. Zuckerberg’s residence. The developer expressed interest in building a nearly 10,000-square-foot house on the property.

But late that year, he offered to sell a small section of the property to Mr. Zuckerberg as a way for the Facebook chief to have more privacy.

A meeting that took place at Facebook headquarters in Menlo Park, Calif., on Dec. 4, 2012, lies at the heart of the suit. Mr. Voskerician contends that he discussed a deal to sell his interest in the entire property, not just part of it. In exchange, he says, Mr. Zuckerberg would make introductions between him and powerful people in Silicon Valley, potential future business partners and clients.

But Mr. Voskerician claims in the suit that Mr. Zuckerberg did not follow through. The latest documents, filed on Wednesday, find some corroboration for that position in the form of a sworn declaration by John Forsyth James, a real estate agent for Mr. Voskerician. The declaration was filed by Mr. Voskerician’s lawyer.

In the declaration, Mr. James said that by the time the meeting took place, Mr. Voskerician had already gotten an offer from another party to take over his contract to purchase the property for $4.3 million — a figure that does not include the actual price of the house. It would have been a huge overnight profit, perhaps reflecting the heat of the market in some of the most desirable locations, rubbing elbows with the technorati.

Mr. James says that at the meeting at Facebook headquarters, Mr. Zuckerberg said he could not match the $4.3 million price. Instead, he expressed an interest in getting a discount on the property and, according to the court filings, “could offer him a relationship if he were to agree to a discount,” Mr. James said in his statement. The statement reads that Mr. Zuckerberg “would introduce Mr. Voskerician to other influential people (including persons associated with Google, Facebook and Apple) who might be interested in real estate or other transactional relationships.”

“He indicated that he would refer Mr. Voskerician to others and promote him through his connections, his friends, clients of Facebook and others that Mr. Zuckerberg knew to be influential,” the declaration says.

It says that at the conclusion of the meeting, Mr. Zuckerberg’s real estate agent, Terri Kerwin, said, “Mark always keeps his promises,” according to Mr. James’s declaration. (It was Ms. Kerwin, said Mr. James, who referred earlier in the negotiations to Mr. Zuckerberg as “just a kid.”)

A few days later, the sides reach a deal: Mr. Zuckerberg would pay Mr. Voskerician $1.7 million — a steep discount compared with $4.3 million — to take over the contract to buy the house and, according to Mr. James, would provide the developer a social network. It was not to be, Mr. James said in his declaration: “Ultimately, Mr. Zuckerberg failed to honor his promise.”

In court documents previously filed, lawyers for Mr. Zuckerberg have said that the Facebook chief purchased the right to the adjoining property to protect his privacy. Mr. Voskerician “threatened” to build “a 9,600-square-foot mansion stretching nearly to Mr. Zuckerberg’s property line.”