Unitarians and other opponents of the orthodox Christian doctrine of the Holy Trinity of the Father, Son and Holy Ghost claim that this idea is in fact Tritheism, since these distinct 'personalities' seem to act independently of one another - though not in conflict.
Proponents of the doctrine of the Trinity claim that the three persons do not have separate powers, since they are omnipotent, and do not have separate spheres of influence; their sphere of influence is unlimited. The persons of the Trinity have one divine essence and are indivisible, whereas Tritheism appears to suggest three separate gods. Athanasius of Alexandria attempted to distinguish Trinitariansim from both Tritheism and Modalism in the Athanasian Creed.
At various times in the history of Christianity, various theologians were accused by the church of tritheism, which the church treated as heresy. John Philoponus, an Aristotelian and monophysite in Alexandria about the middle of the sixth century, was charged with tritheism, because he saw in the Trinity three natures, substances, and deities, according to the number of persons. He sought to justify this view by the Aristotelian categories of genus, species, and individuum. Tritheism was revived in the Anglican Church by Dean Sherlock in his "Vindication of the Doctrine of the Holy and ever Blessed Trinity," 1690. He maintained that, with the exception of a mutual consciousness of each other, which no created spirits can have, the three divine persons are "three distinct infinite minds" or "three intelligent beings." He was widely opposed by trinitarians.
The so-called Hindu Trinity of Brahma the creator, Vishnu the preserver and Shiva the destroyer has also been said to constitute a Tritheistic belief-system. Like the Chistian Trinity these beings are understood to work, ultimately, in harmony with one another. However this Hindu trinity does not have doctrinal status as in Trinitarian Christianity. It is simply one of many ways in which the Divine order of the universe may be understood.