The first call came to the hospital at midnight. A despondent female voice, quivering with emotion, told a security guard: "I would very much like to come up and see my baby . . . . I'd like to take her with me."

That telephone call, and two subsequent ones to Shady Grove Adventist Hospital, apparently were the closest contact authorities have had with the person who placed a newborn girl in an unlocked car in Gaithersburg early Wednesday.

The infant was taken to the hospital after Flora Lichaa found her on the front seat of her car, parked in the driveway of her home on Peach Leaf Drive. The infant was placed in an incubator and quickly recovered from hypothermia--a potentially fatal drop in body temperature--that had begun to set in.

Yesterday, the brown-haired, blue-eyed infant was being smothered with attention by nurses at the hospital's maternity ward; strangers have dropped off gifts for her, and dozens of people have offered to adopt her. One woman wanted to take in the baby and her mother.

"She eats well, sleeps well. Every nurse on the staff is her 'mother,' " said Judy Thompson, a nurse in charge of Shady Grove's maternity section. "A baby being abandoned is sad, but the mother's situation is sadder. The baby is being loved and cared for. We're not so certain that's the situation with the mother."

Doctors are concerned that the mother may need medical treatment, for hemorrhaging or other injuries incurred as a result of childbirth. Efforts to locate the mother have failed, even though police have issued statements assuring her that no charges will be placed against her. Police have searched for clues in the neighborhood where the baby was abandoned, and inquired at schools and colleges about pregnant students and at hospital emergency rooms about women seeking treatment for pregnancy related injuries.

No note was left at the scene, but Lt. Robert Hill said a resident of Peach Leaf Drive reported seeing an unfamiliar car about 6:30 a.m. Wednesday, and again about 8:15 a.m., 30 minutes before the baby was found, in the driveway of Lichaa's house.

"I was surprised and shocked," said Lichaa, 33, the mother of a 1-year-old daughter. "Even before I lifted her out, I just ran back into the kitchen. My mother-in-law asked me what was wrong. I said 'There's a baby in my car!' "

About four babies a year are abandoned in Montgomery County, according to Mike Fitzgerald of the county's social services department. Unless the parents come forward, "we're not very successful at finding the mother and father," Fitzgerald said. Fitzgerald said adoption proceedings will begin in three months if the parents are not found.

Det. Wilfried Stuehmeier of the police department's youth division said "It's touching. She's just a beautiful, healthy baby. I don't see how the mother can deny herself of holding her own baby." Stuehmeier and Lt. Hill said they are convinced the mother had good intentions because she chose an unlocked car with a baby seat in it.

"I think it was the mother who called us," said Bob Kelly, chief of security at Shady Grove Hospital, who said the woman he talked to described the baby's clothing perfectly. "She said 'I would very much like to come up and see my baby, but I'm afraid I might be arrested.' " There have been no calls since then. "I waited last night until 1 a.m. and nothing happened," said Kelly.

"Shady Lady" also has been given an official name, Brenda Georgette Ehrlich, selected by Juvenile Court Judge John Tracey. The judge got the first name from the county social worker on the case; the second from Det. Stuehmeier's middle name (George) and the last from the attorney he appointed to watch over her legal rights.