Although the ballpoint theory was discredited, it continued to be used by neo-Nazis in Europe and the United States. Anti-Semitic pamphlets cited in the book show that the neo-Nazis had a larger aim in trying to discredit the diary as a hoax: to ''prove'' that there had never been a ''final solution'' plan to exterminate the Jews.

In addition to offering factual evidence about the diary's authenticity, the book reveals that there were three different versions.

The first was written by Miss Frank; the second was rewritten by her in a more polished style; the third - the one that was published around the world - was collated by her father, Otto Frank, the only member of his family who survived the death camps. Mr. Frank cobbled some parts of her first draft to her revised draft. He also included some loose sheets she had written as part of her diary. These two earlier versions have never appeared before in English. 'Decided to Publish It All'

''We decided to publish it all - her mistakes, additions and deletions,'' Mr. Barnouw said. ''She rewrote her diary in 1944 so people can compare it with her original. Why? She heard a broadcast beamed from London by the Dutch Government-in-exile. The Education Minister advised people in German-occupied Holland to keep diaries as a record of what went on under the Nazis.

''Anne took the words personally. So in the second version, she made improvements in content and language. She thought the diary could become a kind of detective story. She added 'Tales From the Secret Annex' to her diary. In fact, the title of her diary in the original Dutch edition is 'The Annex.' ''

To make her diary even more creative, she changed certain names in her second draft. For example, instead of calling her family Frank, she changed it to Robin; she became Anne Robin. And she attached other fictional names to people who were hiding from the Germans.

After her father returned from Auschwitz, he decided to publish the diary. He included some of the events that she had recorded in her ''Tales.'' He restored the Frank family name that Anne had fictionalized, retained the fictional names that she had devised for other people, pared some of the criticism by Anne of her mother (who had also died in a concentration camp), and deleted some of the entries about her awakening sexual interest. Deletions by Her Father