Families of victims of the "Torso Killer" say they have finally found relief and can move forward knowing justice was finally served.

Richard Cottingham on Monday admitted to multiple murders that happened in Nassau County decades ago.

Nassau District Attorney Anne Donnelly says Elmont resident Kim Tinsley's sister Laverne Moye's body was found in a Rockville Centre stream on June 20, 1972.

From a New Jersey prison, Cottingham admitted to strangling her.

"Today we found closure, we found out who did it and I feel a lot better today than I did 50 years ago," Tinsley said.

Some closure was also felt for three other families, including Jeannie Heinz, whose sister Mary Beth Heinz's body was found in the same stream.

For decades, Heinz never thought her sister's killer would be found.

"Today, me, my friends and family wish to say, 'Thank you, thank you, thank you,'" Heinz said.

Randi Childs called it a "painful day, but it's also a good day."

Cottingham admitted to killing Childs' mother, Sheila Heiman.

Until now, Childs' father, who had discovered his wife's body in their home, was considered a person of interest in the murder.

Childs say her father's reputation has been restored with Cottingham's confession.

"There was nothing really, no reason why he should have been suspected, and my poor dad lived with that until the day he died," Childs said.

Donnelly says Cottingham also admitted to killing 18-year-old Maria Nieves. Her body was found on Dec. 27, 1972 near a bus stop at Jones Beach.

Investigators say they have not been able to find Nieves' family in the United States or Puerto Rico, where she was originally from.

"We are looking, and we hope to give them the same closure some of the other families have received," Donnelly said.

Nassau County detectives say they had a total of 13 cold case murders that Cottingham could have been involved with, but he would only give information on the five to which he pleaded guilty.

Nassau detectives say they will continue to find evidence and pursue the killer or killers in those cases to bring closure to the remaining families.