The surveillance video shows William McQuain, dressed in shorts on an October Saturday, rolling around the parking lot of a Germantown self-storage warehouse on the wheels in his sneakers.

“He was behaving like a typical 11-year-old,” said Montgomery County Police Chief J. Thomas Manger. “Gliding up and down the pavement.”

What the 11-year-old didn’t know, authorities said, was that his mother had been beaten and stabbed to death in their nearby apartment. William was at the storage center happily waiting with the man police say killed his mother — Curtis Lopez, his stepfather.

By the end of the day, Oct. 1, police said, Lopez would also kill William and toss his body in the woods.

For days, police and volunteers conducted a massive search in hopes the boy would be found alive. Friends gathered for a vigil, and his football buddies put stickers on their helmets: “William McQuain. WeU.” But Tuesday morning, hope turned to mourning when police said the boy’s body had been found in a wooded area just off a Clarksburg road. Detectives had focused on that area after tracking Lopez’s cellphone use.

“This confirmed our worst fears,” said Jeff McDermott, who coached William on a Little League All-Star team. “He was a great kid, a great player. He did everything we asked him to do.”

Lopez and Jane McQuain had a long and troubled relationship, but only days earlier the two had taken William on a vacation to Ocean City. A friend said Jane McQuain called from the beach, saying that she and Lopez had argued and that she was scared.

Exactly what happened that weekend might never be known. Lopez, who was arrested Thursday in North Carolina, has refused to talk to investigators, police said. The police account of what happened to William and his mother is based on the evidence that had been gathered. Lopez has been charged with murder in the slaying of McQuain, 51, and police said they expect to charge him with murder in William’s death.

Montgomery police were first called to McQuain’s Germantown apartment last Wednesday by a friend who was worried after she had been out of touch. Officers who climbed a ladder and crawled through a window found McQuain dead in her bedroom. There was no sign of William, nor any sign that he had been hurt in the apartment.

But there were plenty of signs of him and accomplishments: Photos and certificates hung throughout, an indication of a single mother whose life revolved around a quiet, sharp kid with a sweet disposition.

“The apartment was like a shrine to him,” a law enforcement source said.

An acquaintance of McQuain’s told police about a man seen going in and out of her apartment, according to court papers posted online by WUSA-TV (Channel 9). A neighbor saw the man load a TV box into McQuain’s sport-utility vehicle. That man was Lopez, court papers said.

Police found Lopez last week after McQuain’s 2011 Honda CRV had been in an accident in Charlotte, according to the court papers. The woman driving the Honda said she was Lopez’s girlfriend and told police that she was driving her boyfriend’s mother’s car and that the mother’s name was Jane.

The next day, Oct. 13, authorities found Lopez and the woman at a hotel in Charlotte. Lopez’s girlfriend told police that he had taken an Amtrak train to Philadelphia in September to visit family, according to the warrant. He returned driving the Honda and brought back a large television in a box and an Xbox video game system, the warrant says.

Officers found one of McQuain’s credit cards and a box cutter in the hotel room, the warrant says.

Montgomery detectives went to Charlotte to interview Lopez, but he refused to cooperate, said Capt. Paul Starks, a spokesman.

So officers tracked Lopez’s movements in Montgomery using cellphone records, according to sources and court records. Dozens of officers and volunteers began searching woods in the Clarksburg and Damascus areas. On Tuesday, a search dog led to the body of a boy.

Police officials said it was William. He appeared to be wearing the same clothes as in the video. His body was covered with brush, Manger said.

Officers and detectives had tears in their eyes. They’d hoped, even as the evidence mounted against it, that they would find William alive. Manger said he prayed for William at Sunday Mass.

McQuain’s brother, her only close living relative, declined to comment Thursday, noting his deep grief.

Family friends described William, who grew up without his biological father in his life, as a smart and athletic child who was always by his mother’s side, a boy who impressed people with his good manners and attitude.

“Will knew as a little kid that he was a good-looking young man, and he always loved to pose for pictures,” said Ronald McCombs, who helped raise William in his early years when he was in a relationship with Jane McQuain. “He was a great kid, the kind of kid you hope for.”

McCombs said he was leafing through William’s old drawings and awards — including one from second grade at Gaithersburg Elementary School, when he won “most improved attitude and effort” — and fighting back tears.

It was McQuain’s hope that William would grow up without the problems that plagued her early adulthood, including running with a rough crowd, overindulgence in alcohol and eventually stretches of homelessness. William’s birth changed her, friends said, and she did everything in her power to keep her past away from William’s present and future.

Family friends said McQuain had been trying for years to keep Lopez at a distance because of his violent history. Convicted of attempted murder in 1987 for stabbing a man, Lopez served a prison sentence in Pennsylvania. McQuain, who married Lopez and testified on his behalf at trial, would occasionally visit him in prison.

After William’s birth, McQuain was determined to leave it all behind. She quit drinking, got a steady job and concentrated on William. She decided that she didn’t want a man living with her because she feared bad influences.

“Jane didn’t want anything bad around William, so she got a two-bedroom apartment, one room for her and one for him,” said a close family friend who spoke anonymously because she fears retaliation. “William was her everything.”

McCombs said that after Lopez was released from prison, he tried to get back into McQuain’s life. The family friend said Lopez would spend time with McQuain each summer.

McCombs said he spoke to McQuain on Sept. 30, when she called from her cellphone to say that she and Lopez had been arguing. Lopez, McQuain, William and a friend of his were in Ocean City and were preparing to return that day to Germantown, McCombs said.

“She stepped away from him and called me to tell me that she was afraid,” McCombs said. “I’d never heard Jane talk like that.”