When did it get started? Pretty much from the beginning. Gregory of Nyssa (died around 386) wrote an apologia entitled "
On Not Three Gods."
When the Church's language made the shift from Greek to Latin, the "Fathers" began to use the Latin word "persona" instead of the Greek "prosopa."
Though both words had a similar meaning, in Latin philosophy "persona" was already developed to include the idea of "separate beings." The Greek "prosopa" didn't carry that baggage. So, in the West there was an almost immediate argument from some that the "Orthodox Christianity" of the Old Catholic Church was "tritheistic." Certain "heretics" of that time made the claim as did Jews and later Muslims. Many pagans remarked on what they saw as an inconsistency within Christian philosophy.
In many places orthodox believers themselves sometimes tended toward a tritheistic outlook as opposed to "what they're supposed to believe." Concerning Jesus Christ, the Nicene Creed states:
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And in one Lord Jesus Christ, the Son of God, begotten of the Father [the only-begotten; that is, of the essence of the Father, God of God], Light of Light, very God of very God, begotten, not made, being of one substance with the Father;
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Today it's stated as,
"God from God, Light from Light, True God from True God..."
Add to that,
the Holy Spirit,
Quote:
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the Lord and Giver of life, who proceedeth from the Father and the Son, who with the Father and the Son together is worshiped and glorified, who spake by the prophets...
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and it's easy to see how even many Trinitarians get a tritheistic view. The language of the creeds inherently lends itself to the idea of "three seperate Beings who are all called "God."
The charge of "Tritheism" has been repeated by many since antiquity.