Jesus and Contingency Let's assume that God is omnipotent in the sense that he can do anything which is logically possible (so that he cannot create square circles because  a square circle is a contradiction).

Now it is thought that God cannot do things like make himself cease to exist, or to become contingent. How does this square with the idea that (at least some part of) God became a man. By entering into time and assuming a bodily form, is that not the meaning of becoming contingent? 

I can anticipate the answer that Jesus has two natures, the human one that is contingent (and does not exist anymore) and one that is divine (which was never contingent), but this seems to me to just split Jesus into a divine part (which was never contingent) and the ordinary human part, so that the Jesus that walked on Earth was an ordinary human, and hence no need fore the idea of the trinity. 

Any way to resolve this dilemma?

Edit: Perhaps to restate: Do we have to accept that God - in his omnipotence, must be able to create the logically impossible, in order to believe in something like the trinity?
Not in the slightest. The Incarnation does not involve the assumption of contingency. The Incarnation adds nothing to the person of God the Son, only to creation (inasmuch as the human nature of Jesus is a creature).

That is, the soul created for Jesus, is Jesus' soul, but in not too dissimilar a way to how creation is God's own also, created for Him. When God creates souls, He by so doing, or perhaps simultaneously, creates a new person that this soul is the soul of. However, in the Incarnation, God created a soul for Jesus, which assumes His Person, instead of a created person.

The very fact that Monophysitism is a heresy proves that contingency is not affected, for the divine and human nature of Christ are not mingled, and there is absolutely no admixture or confusion of natures (Monophysitism meaning, 'One-natureism,' referring to the heretical idea that Christ's divine and human nature melded into one Supernature).

Truly, the human nature of Christ is a Tabernacle: "the Word became flesh and tabernacled among us" (John 1:14). (I don't intend to give the impression it was a puppet for the Son, but rather a vehicle for His Person, or a mode of living on earth; the former would be heretical.)

In other words, in the Incarnation, nothing is added or which, taken away, changes Who or What he was before. That is, the Hypostatic Union (meaning the unity of natures in the one person of Christ) could theoretically be undone, and Christ's human nature destroyed; inasmuch as it was not necessary for Him to be incarnate in the first place).

Also, Christ's human nature still exists. It didn't get destroyed.