Family roots go as deep as granite in church files

Your name - along with almost every other name ever been recorded on earth - will likely be on file someday at the genealogical files of the Mormon church.

So vast are the pedigree records here that the church is building a bigger, better-organized library, starting this fall. The vital statistics of over a billion people from dozens of countries have been collected so far. In addition, over 160,000 books on separate family trees have been shelved. By 1986, more than 100 computers will be linked up to the records, helping visitors quickly climb up and down their family tree.

''We get some complaints that we are 'Big Brother' keeping tabs on everyone, but that is not our intention,'' explains Tom Daniels, spokeman for the genealogical library.

Rather, members of the church use the record of names to posthumously baptize the dead into the Church of Latter-day Saints of Jesus Christ (Mormon), based on the theological justification that each family will be reunited after death.

The practice of genealogical record-keeping first became popular in the church during the 1890s. Today, over 1.25 million rolls of microfilm - each 100 feet long and with about 1,200 pages on each - are stored in the library, with master copies placed in 600-foot-long granite tunnels in a mountain near Salt Lake.

In 1977, after the showing of the TV movie ''Roots,'' the number of library visitors here doubled. Average patronage is now 3,000 a day, and several dozen consultants have opened businesses to help people dig their family roots. The library staff of over 500 workers, plus about 400 volunteers, is being supplemented by church workers around the world who help screen out names from raw records.

The collection of recorded names is not limited to Mormon families, nor to the United States. A team of church officials, using some 100 cameras, is filming such documents as land grants, census records, birth and death records in about 40 nations, with careful negotiations conducted first. Records from West Germany, Mexico, Hungary, and the Scandinavian countries are virtually complete, Mr. Daniels says. So as not to appear to be ''snooping'' on living people, the library generally accepts only records starting before 1900.