Did our Lord Jesus Christ have all the three components of any human body: body, soul and spirit? What was the role of the Holy Spirit then?
Our Lord Jesus Christ was incarnate and took the form of a complete man with body, soul and spirit. To say that our Lord took only flesh and soul but had a divine Spirit is totally wrong. The Holy Scripture holds that the Logos assumed all that is human including the spirit and that He experienced joy and sadness, both being properties of the spirit. Christ without a rational spirit is not a man.
In the third century, the heresy of Apollinaris also known as Apollinarianism called a similar belief. Apollinaris, bishop of Laodicea, considering the spirit as essentially liable to sin, saw no way of saving our Lord Jesus Christ's perfection and the infinite value of Redemption, except by the elimination of the human spirit from Jesus' humanity, and the substitution of the Divine Logos in its stead. For the constructive part of his theory, Apollinaris appealed to the well-known Platonic division of human nature: body, soul, spirit (nous, pneuma, psyche logike). Christ, he said, assumed the human body and the human soul or principle of animal life, but not the human spirit. The Logos Himself is, or takes the place of, the human spirit, thus becoming the rational and spiritual centre, the seat of self-consciousness and self-determination. By this simple device the Laodicean thought that Christ was safe, His substantial unity secure, His moral immutability guaranteed, and the infinite value of Redemption made self-evident. Apollinarianism was condemned in the council of Constantinople 381 A.D. "We pronounce anathema against them who say that the Word of God is in the human flesh in lieu and place of the human rational and intellective soul. For, the Word of God is the Son Himself. Neither did He come in the flesh to replace, but rather to assume and preserve from sin and save the rational and intellective soul of man."
The incarnation is the work of the Three Persons of the Trinity. The Father sent His only begotten Son to redeem us "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life" (John 3:16). The Son, the Logos was incarnate "And the Word became flesh and dwelt among us" (John 1:14), and it is by the action of the Holy Spirit that St. Mary conceived our Lord Jesus Christ (Lk 1:35; Mt 1:18).
This Q&A was found on Archangel Michael & St Bishoy Coptic Orthodox Church : http://www.stbishoy.org.au/modules/smartfaq/faq.php?faqid=79