(04-16) 18:38 PDT SAN FRANCISCO -- A 12-year-old San Francisco girl missing since Monday is a possible runaway who may be staying with a man, police said Wednesday, a theory that one relative denounced as "lies."

Family members continued to scour the neighborhood in Balboa Park where Billie McGee was last seen and said they feared she had been kidnapped.

Police Capt. Marsha Ashe, head of the police juvenile division, said officers were also concerned for the girl's well-being and said investigators had concluded that she was "possibly a runaway."

Ashe said the girl was "sophisticated beyond her age" and had been in contact with men while using the name "Tania." Investigators think she may be with an older male, Ashe said.

Police said the girl's mother had intercepted text messages intended for Billie that had sexual overtones and that the two quarreled Monday. The child then left her family's home near City College, investigators said.

Family members insisted Billie was a good girl and an honor roll student with no history of problems who wouldn't have run away.

"These are lies," her aunt Theaster McGee said. "Billie is a 12-year-old child. ... She ain't done nothing with no men. Come on now."

She said Tina Brown, the girl's mother, had never intercepted text messages intended for Billie. Brown was not available for comment Wednesday because she was out posting fliers of her missing daughter.

McGee said she was the last person to speak to Billie before she left for school Monday. The girl and her mother never quarreled about a man or text messages, she said.

"Billie's a good kid," her aunt said. "These are all lies."

Billie, a seventh-grader at S.R. Martin College Preparatory School, planned to catch a Muni bus to school Monday morning, her family said. Her mother often drives Billie to class, but called that morning to tell the girl that her graveyard shift at San Francisco General Hospital was running over its scheduled time, relatives said.

Brown said Tuesday night that she feared someone had kidnapped her daughter.

Ashe said police have interviewed several men with whom the girl had been in text-message contact. "They were all surprised to find out she was 12," Ashe said. "She presented herself to be much older."

Ashe added, "I'm concerned for her. I hope she comes home. We want to make it possible for her to come home."

Billie was last seen wearing her school uniform: a black-and-white jacket with a white collared shirt and black pants. She is 5-foot-5, African American and weighs 140 pounds. She has black hair and brown eyes.

Anyone with information is asked to call the police missing persons unit at (415) 558-5508 or the department's operations center at (415) 553-1071.

E-mail the writers at jvanderbeken@sfchronicle.com or cvega@sfchronicl.com.