Alec Baldwin and Fiancee Hilaria Thomas Pack on PDA in Rome

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Now that's amore. Alec Baldwin and his new fiancée Hilaria Thomas packed on the PDA during a getaway to Rome this week. Forget holding hands, the two lovebirds — who just got engaged in early April — were so caught up in the romance of the Italian capital, the "30 Rock" star even dipped Thomas and gave her a giant smooch right in the middle of a crowded street! And the excitement was mutual. "Good food, vino, cafe, familia, museums, siestas … I can't wait," the 28-year-old yoga teacher tweeted just before they took off from their New York City home base.

The Italian trip is a mix of both business and pleasure for Baldwin. The actor, 53, is also promoting his new movie, the Woody Allen-directed "To Rome With Love," which also stars Penelope Cruz and Ellen Page and hits theaters in Italy on April 20.

But it's his other acting job, as eccentric network executive Jack Donaughy on NBC's "30 Rock," that has everyone buzzing right now. On Wednesday, right before he jetted off for Italy, Baldwin tweeted, "I think I'm leaving NBC just in time," which caused much confusion. While he reportedly meant the message to be about a crew for "Today" arriving at his apartment building, many fans took the cryptic message as a hint that he was leaving the Emmy-winning comedy starring Tina Fey and Tracy Morgan.

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Fey, the show's creator and head writer, was quick to dispel the rumor. Baldwin, who has one more year left in his contract, "is not leaving the show," the former "Saturday Night Live" star explained during a Thursday appearance on "The View." "We're all in this together till the end. I think he just maybe means that the end of the show is visible on the horizon. We can't do this for 35 years. We'd love to keep going and kind of see where everybody ends up, but you don't want to see me with a gray stripe [in my hair], eating a slice of pizza, going on dates."

Yes, Tina, we actually do!

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