Almost immediately after her second birthday, my daughter's favorite book became ''The Runaway Bunny,'' the Margaret Wise Brown classic first published in 1942. No matter where the little bunny hides or how far it runs away, the mother bunny always finds it.
For 2-year-olds -- who want desperately to be independent one minute, and to be protected the next -- ''The Runaway Bunny,'' (Harper & Row paperback, $3.50) is as reassuring as a hug. Now there's a new book that conveys the same kind of comforting message to children who are testing their limits (and trying their parents' patience).
''Mama, Do You Love Me?'' by Barbara M. Joosse, illustrated by Barbara Lavallee (Chronicle Books, $12.95, ages 2-6) captivates adults and children alike. The mother and child in it are Inuit -- the native name for the Arctic people usually referred to as Eskimos.
The author and illustrator carefully researched the Inuit culture, capturing a traditional way of life that is swiftly vanishing. Ms. Lavallee's watercolors are as bright as the Northern Lights.
The little girl in the story asks a series of questions to see just how far she can go. ''What if I put salmon in your parka, ermine in your mittens, and lemming in your mukluks?''
''Then I would be angry,'' her mother says.
''What if I threw water at our lamp?''
''Then, Dear One, I would be very angry. But still, I would love you.''
''What if I ran away?''
''Then I would be worried,'' her mother says.
''What if I stayed away and sang with the wolves and slept in a cave?''
''Then, Dear One, I would be very sad. But still, I would love you.''
And so it goes. A glossary gives adults an explanation of the animals and domestic items introduced in the story, such as lemming and mukluks.
One piece of advice: Always read this book with a child in your lap, so you're ready for the big hug that comes at the end.
* Another fun book for moms and kids is ''Where's Our Mama?'' by Diane Goode (Dutton, $13.95, ages 3-7). Set in Paris in the early 1900s, this is the story of two young children who get separated from their mother at a train station.
A gendarme comes to their aid, and the three of them set off to find Mama. What does she look like, the gendarme asks. ''Our mama is the most beautiful woman in the world!'' the children tell him.
He takes them to a ravishing model. No, the children say, that's not her. Following their clues -- she reads millions of books, she is famous for her voice, she cooks the best food in the world -- the gendarme takes them, in turn, to a librarian, an opera singer and a chef. No, no, no.
Finally, they return to the station, where the real Mama -- sweet and ordinary, but in her children's eyes so extraordinary -- has been waiting.
Ms. Goode, whose illustrations made ''When I was Young in the Mountains'' a Caldecott Honor Book, went to Paris to research the scenes in her paintings. It's a lovely book.
* Another recent picture book celebrates grandmothers. ''Abuela'' by Arthur Dorros, illustrated by Elisa Kleven (Dutton, $13.95, ages 3-8) will look familiar to fans of ''B is for Bethlehem,'' the Christmas alphabet book written by Isabel Wilner of Towson and illustrated by Ms. Kleven.
Ms. Kleven's style is unmistakable: folk-style painting in the colors of jewels, textured with cut-paper collage in intricate, whimsical detail.
Mr. Dorros, who wrote ''Tonight is Carnaval,'' introduces readers to Hispanic culture by way of an adventure, not a lesson. A young girl and her grandmother -- Abuela in Spanish -- get on the bus for a jaunt across New York City.
Imagining that she and her Abuela can fly, the little girl soars over Central Park, past elevated trains and the office building where her father works, around the Statue of Liberty and then down to her aunt and uncle's grocery story, where the girl and Abuela stop for a cool limonada.
Mr. Dorros intersperses Spanish words and phrases, always offering the English equivalent. Kids are quick to pick up on other languages, and they'll have fun mastering words that give their parents fits.