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By Candace Smith and Carlos Boettcher

It is the battle of the millionaires … over what? More money, of course.

Linda Evangelista and her former beau Francois Henri-Pinault faced off in court in New York on Thursday afternoon in a bitter child-support dispute over how much money Evangelista will receive to take care of their 5-year-old son, Augustin.

In the first day of this explosive hearing in a Manhattan Family Court, Evangelista, 46, denied accounts that she was demanding a record-breaking $46,000 in monthly expenses from Pinault,  audibly crying out after David Aronson, Pinault's attorney, asked if she was asking for that amount of money. Her team said that they had never asked for that specific amount, claiming that the media was spreading misinformation.

If the judge awards that amount- the equivalent of $1,500 a day- Pinault, heir to a $1.5 billion family fortune, would break New York state's record for the biggest child support payout, a record now held by Sean "Diddy" Combs, who pays $19,000 in monthly expenses.

Evangelista,  donning oversized sunglasses and python Christian Louboutin stilettos, strode into court almost 20 minutes after the hearing was scheduled to begin, barely casting a glance at her former lover.

She and her lawyer, William Beslow, asserted that, in the context of Pinault's great wealth (he earns $5 million a year), he has paid nearly nothing to support little Augie. Her defense team claimed that Pinault asked her to terminate her pregnancy. According to her lawyers, she refused and said that she would pay child support herself.

The supermodel, whose face has graced more than 600 magazine covers, is worth about $8 million.  But she says now that her lucrative L'Oreal Paris contract has ended, the time has come for her to seek child support. She says that she first filed for child support in 2010 and then again in 2011. Both of her claims went unanswered, she said.

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Pinault, after taking the stand, vehemently denied claims that he asked Evangelista to abort the baby and countered by saying he tried several times to put forth child-support plans and was met with either total unresponsiveness or merely unreasonable demands.

"I was not involved in the decision of having a baby," he said.

Evangelista insists that she needs the money for around-the-clock care for Augie as well as a driver and armed bodyguards for her son. She's also asking for Augie to be cared for as lavishly as Pinault treats Valentina, his daughter with his wife, actress Salma Hayek.  Pinault has a $13 million California mansion in a trust for Valentina and, according to the New York Post, Evangelista is asking for at least a country home for Augie.

Divorce lawyer Raoul Felder told ABCNews.com that he believes Evangelista's requests are unlikely to be fulfilled.

"It's the triumph of illusion over reality," he said. "That's all this is, a fairy tale."

"If she were married to him, that's a whole other story," he added.

Evangelista and Pinault dated for four months beginning at the end of 2005, and she was pregnant with Augie when Pinault began dating Hayek in 2006. Pinault and Hayek married in 2009.

Pinault says that he will not pay anything until the court renders a decision. The hearing is slated to continue through Tuesday.

ABC News' Luchina Fisher contributed to this report.