Though she’s not one of the onscreen parents who topline NBC’s “Up All Night,” it’s hard to imagine the show without Maya Rudolph.The series focuses on Christina Applegate and Will Arnett juggling a baby and a robust career. And as Rudolph says, that’s the way the original pilot looked. But Rudolph, a veteran of “Saturday Night Live” and co-star of “Bridesmaids,” was approached early on by creator and former “SNL” writer Emily Spivey about hopping on board. “Emily’s been creating roles for me for the last 15 years, since we did the Groundlings together,” Rudolph says. “She knows my voice really well, so I took a big leap of faith.” Rudolph’s character went through a few iterations. In an early pilot, she helmed the public relations agency that Applegate’s character worked at, but then exec producer Lorne Michaels stepped in, having seen Rudolph impersonate Oprah Winfrey numerous times and a talkshow host was born. Rudolph took care not to bring much of her Oprah to the role of Ava, preferring to approach the character with a fresh slate. “I still don’t know who she is; a totally bizarre made-up character — selfish, but weirdly sweet and well-intentioned. And because she’s not based in the real world, she had the freedom to be strange. It’s a good combo with the others on the show, who the audience can identify with,” she says. Every comedy needs a straight man and a funny man, and Rudolph has positioned herself as the perfect foil for “Up All Night”: dynamic, larger-than-life, sometimes wacky. The role might not have been in the original show pitch, but it has become essential.