July 31, 2008 08:30 AM

After nearly four weeks of silence, New York Yankees slugger Alex Rodriguez stepped up to the plate Thursday and responded to his wife’s demand for divorce.

In the documents – filed Thursday morning – A-Rod admits the marriage is “irretrievably broken.” But he points out that Florida is a “no fault state” and chastises his estranged wife, Cynthia Rodriguez, for mentioning “immaterial and impertinent” issues like his alleged “extra marital affairs and other marital misconduct.”

Although Madonna was not mentioned in Cynthia’s court documents – filed July 7 – her attorney called the Yankee’s association with the singer an “affair of the heart” and “the last straw.”

In Cynthia’s filing – which claimed “emotional abandonment” – she asked to keep their $12 million Coral Gables mansion. The mother of his two children, Natasha, 3, and Ella, three months, also wants a cut of his earnings during their marriage.

But, in A-Rod’s response, he argues that the divorce settlement should be determined by their prenup, which Cynthia signed a month before their 2002 wedding.

According to the documents, she did so “with the assistance of counsel of her own choosing, freely and voluntarily … and with full and complete financial disclosure of husband’s income, assets and liabilities.”

Regarding the children, A-Rod seeks shared parental responsibility for their “wealth, health, education and religious upbringing.” (There’s no mention of Kabbalah, the mystical Jewish teachings that, sources say, helped foster a bond between A-Rod and Madonna. The pop icon has denied the alleged affair.)

A-Rod admits Cynthia is a “loving and nurturing mother.” In the filing, he suggests the two work out a time-sharing custody schedule without the court’s intervention.

According to his attorneys, Alan Kluger and Jason Marks, “husband requests that both parties are designated as ‘co-residential’ parents, realizing that the children are likely to spend more time with wife given the realities of husband’s professional life.”

A-Rod acknowledges he should pay child support – and asks the court to determine a fair amount.

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