"The DNA tests provided decisive evidence that the six children that Elisabeth gave birth to have the same father," said Lower Austria police chief, Franz Polzer.
Police still want to know however how Josef Fritzl was able to dig a warren of rooms extending under his house and garden, and bring up three children who had not seen the light of day until recently, without the rest of his family or the neighbors ever finding out.
The Austrian media, which has dubbed the family's dungeon a "House of Horrors", has also been asking why Fritzl, who had a previous rape conviction, was allowed by the authorities to legally adopt three of his grandchildren - also his children - when he brought them out of the cellar and claimed they had been left by their mother, who had been missing since 1984.
The only image so far released to the media of Elisabeth Fritzl shows her as a smiling teenager with braces. Eyewitnesses say that after living most of her life underground, and being routinely raped by her father, she is now a withered, white-haired, terrified woman. She only agreed to answer police questions on the firm condition that she would never have to see her father again.
Apart from the six children that Fritzl is known to have definitely fathered with his daughter, he is also said to have incinerated another that died shortly after being born.
Fritzl also fathered another seven children above ground, prompting Frank Polzer, the head of lower Austria's criminal affairs office, to describe him as "extraordinarily sexually potent".
Of the three children that until last week had never known life outside their basement, five-year-old Felix Fritzl seems to have fared the best. Polzer described the boy's excitement when he got to ride in a police car, something he had only seen on television, the family's only contact with the outside world.
The case came to light when the oldest of the three, 19-year-old Kerstin, fell gravely ill and was brought out by Fritzl and admitted to hospital. She soon fell into a coma, and after a note written by her mother was found on her, doctors issued an appeal for Elisabeth to come forward.
Fritzl then released his captives, explaining to his astonished wife that her daughter had decided to return.
On being questioned by police he came clean about the underground prison, and gave them the code to the lock on a one-meter-high steel door in his garden shed, the only entrance to the basement.
Inside, investigators found a network of small rooms covering a total area of about 60 square meters, with ceiling height of 1.7 meters (5 foot 6 inches). The interior includes a kitchen, a boiler room, a padded cell with soundproofing, a bathroom decorated with octopus stickers and a toy elephant, and two bedrooms.
Above ground the house had also been substantially extended to accommodate Fritzl's ever-expanding family, jutting out well into the garden behind the row of terraces in the small picturesque Lower Austrian town of Amstetten, located 130 km (80 miles) west of Vienna.
The case has prompted parallels with the abduction of Natascha Kampusch, who escaped from her captor in Vienna in August 2006 at the age of 18, having been held captive in a the cellar below the garage of technician Wolfgang Priklopil for eight years.
