This article is from the Star Trek Tech FAQ, by Joshua Bell inexorabletash@hotmail.com with numerous contributions by others.
For better or worse, no such device has been intentionally created by
24th century science. However, in "The Enemy Within" [TOS], Kirk's
duplication may have been caused by some accidental effect which
caused an ACBS to form in the normal transporter mechanism, with
disastrous results. The Encyclopedia says that damage to the the
transporter's ionizer was the cause of the split.
In "Second Chances" [TNG], the mechanism by which Riker is duplicated
is explained in detail. During transport through severe atmospheric
interference, the transporter chief locked onto Riker's signal with a
second ACB. When it turned out not to be needed, the second signal was
abandoned. The atmospheric interference caused the second ACB to be
reflected back to the planet, and somehow the matter stream was
duplicated, using phased matter from the atmospheric interference
effect to provide the duplicate mass.
 
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