Can you just imagine the baby crafts? Can you?!

The world's foremost domestic diva added yet another title to her empire Tuesday, as Martha Stewart became a first-time grandma to a baby girl born, after a public and lengthy struggle, to her only daughter, Alexis, via a gestational carrier.

But if you think she's going to tolerate being called "grandma," you've got another thing coming. So what's her preferred sobriquet? And, more importantly, what's the little girl's?

Alexis Stewart, Martha Stewart

Brian Killian/WireImage

Cue the swelling of Beatles music: it's Jude!

"I am really thrilled to share some very exciting news with you," Martha said on today's Martha Stewart Show. "At 12:58 a.m. on March 8, little baby Jude, my first grandchild, was born. It's very exciting and Alexis and the baby are doing very well.

"They're home in New York in their apartment and I stopped in last night after a business trip and I got to see her when she was about 36 hours old—she is very alert and doesn't cry. Ideal baby...I'm happy for Alexis that she doesn't cry...and she is eating well and donig all her natural things and she's cute and she has Lexie's pouty little mouth. Very, very lovely child.

"Good luck baby Jude and good luck Alexis. You're on to the next phase of your life—motherhood."

It's a phase that Alexis has been eager to get to, as the 45-year-old has been open about her years-long struggle to conceive a child, even detailing her $20,000-a-month fertility treatments on an episode of The Oprah Winfrey Show back in 2007.

As for baby Jude, Alexis announced on her satellite radio show Whatever with Alexis & Jennifer that her daughter was born at one in the morning, and that her arrival was quickly heralded by Martha, who brought over a "huge box" from Bergdorf Goodman. But Alexis doesn't plan on going the spoiling route with her daughter.

"I'm like, 'Wow, I guess I'm going to be allowed to buy myself something pretty nice because all this stuff's going back!' " she said. "If the kid can't see it, why the $100 clothes?"

As for Martha, well, if you can't imagine her being referred to as grandma, you're in good company. So what will it be—grandmother? Granny? Grams?

"Martha is going to be called 'Martha,' " Alexis announced.

But of course.

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