SHOCKING DETAILS have emerged in the case of GENEVIEVE SABOURIN, ALEC BALDWIN’s alleged stalker including her rage at his engagement and secret baby plans during what her lawyers call an “affair”.

Sabourin, 40, who arrested yesterday for allegedly stalking the “30 Rock” star claims that they were lovers and that she wanted to have his baby, while he admitted to cops to wining and dining her — in a “strictly professional’’ manner, The NY Post reported.

Baldwin told detectives he was merely trying to help French-Canadian stunner some movie roles in the United States when he took her to dinner in 2011 twice, insiders told the NY tab.

Yet Sabourin who was collared outside Baldwin’s posh Manhattan apartment building Sunday night, claims their relationship was more than business

After the news broke that Baldwin, 54, was engaged to 28-year-old yoga instructor Hilaria Thomas, Sabourin went berserk, sources said.

“The suspect said they had sex and she wanted to have his baby,” a law-enforcement source divulged. She also claimed she and Baldwin were lovers.

Sabourin, who speaks French, bombarded Baldwin with English-language e-mails, including one April 4, “I need to start my new life, with my new name . . . in my new country help me my newly (sic) husband, you!”

But when police initially questioned Baldwin he denied having any affair, saying he had only taken Sabourin to sinner, insisting the eat-and-greets were “strictly professional”, denying any “physical relationship”.

According to the criminal complaint, the pair dined “briefly’’ in 2010.

It remains unclear whether Baldwin had supped with the shapely blonde after he began dating Hilaria Thomas last May.

At her client’s arraignment in Manhattan Supreme Court, Sabourin’s lawyer, Julie Sender, said that the pair had a two-year relationship.

“They met. They had dinner. They had a mutual relationship, with texts, e-mails going in both directions,” the lawyer said.

Baldwin and Sourbain met on the set of “Pluto Nash” – he had a bit part and she was the unit publicist on the Eddie Murphy flop.

Baldwin’s rep denied Sabourin’s claim that she and Baldwin were lovers.

“We’re not responding to questions about the ongoing investigation,” Matthew Hiltzik told media.