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Yes, great quote In Principio.

But it must be believed without doubt that true conversion supplies for Baptism of water when, not of contempt, but of necessity some die without Baptism of water.  It is expressly stated, Ezech. 18, if the wicked do penance for all his sins, I will not remember all his iniquities.  Thus also Ambrose clearly teaches in his oration on the death of Valentinian the younger:  Whom I was, he says, about to regenerate, I have lost; but he did not lose the grace which he had hoped for.  Thus also Augustine lib.4. de baptism, cap.22. & Bernard epist.77 & after them Innocent III. cap. Apostolicam, de presbytero non baptizato, whence also the Council of Trent, Session 6, Chapter 4 says that Baptism is necessary in fact or in desire.

As you say, these giants of the Church not only teach it, but they explicitly say that Trent teaches it. It's there in black and white, but so many members of this forum prefer their own "understanding" of what Trent teaches. How is it possible? It is just incomprehensible to me, it just beggars belief.

We believe that St. Robert Bellarmine was wrong on this point, and so did St. Peter Canisius, who authored one of the most famous and papally-approved Catechisms in Church history, actually cited the Council of Trent as REJECTING Baptism of Desire.  But you won't see any of St. Peter's citations quoted by the BoDers, since they fitler out anything that doesn't line up with their agenda.  St. Peter Canisius was present at Trent and was considered one of the top theologians in the Church.

You've made up your mind ahead of time and proclaim "Great Quote" when something agrees with your predetermined conclusion, but then filter out anything to the contrary.

St. Robert Bellarmine was mixed up here.  Desire can supply for Baptism, he says.  Supply how?  Baptism has two effects, the remission of sin and the conferral of the Baptismal character.  So it doesn't fully supply for Baptism.  None of this is clearly elaborated, and the part of St. Robert's opinon that is almost never cited by BoDers is where he gives his reasoning that Catechumens can be saved in this manner (note, no one else, because he strongly believed in the Church being a visible society, some later would argue that this was to a fault), the part that's never cited is where St. Robert gives his reasoning as that "it would seem too harsh" to exclude Catechumens from the possibility of salvation ... so emotional theology, which is what St. Augustine clearly states gave rise to BoD theory in the first place.

A Protestant, is possibly/likely baptised, in which case BOD would not apply, but who can know if a Protestant is "unrepentant" when he dies? Who knows the state of any soul entering their eternity? God alone, unless by special revelation.

Cromwell, being a Puritan, was also almost certainly baptised.

Stalin and Hitler were born Catholics and surely received the sacrament of baptism. You definitively exclude the possibility of their conversion, the possibility that they died in God's grace? That is not Catholic. Admittedly, who would want to be in their shoes? But that is beside the point.

The infidel, the pagan? Let it suffice to say, that if they are saved, it is only in and through the Catholic Church. Imagine some pygmy in a rainforest in deepest darkest Africa isolated from all civilization, let alone Christianity. Did God create this soul? Does He have an infinite love for them? Does he not desire the salvation of that soul that He created infinitely? Will He not give them the means to attain the end for which He created them, and which He Himself infinitely desires? Given that the Church teaches BOD, obviously God does save souls without the ordinary means of sacramental baptism. Now if a soul like this, in invincible ignorance, seeks and desires God and wants with all his heart to know and love and obey Him, will God not take this desire, just like He takes BOD, for the reality of Charity and take that soul to rejoice with Him in the blessedness of Heaven? No one is saying it is not rare. No one is denying EENS. God's mercy is infinite. That does not deny His Justice. Any soul, whoever and wherever they may be, that truly seeks God in this life, whether they be Catholic, Protestant, Jєω, Moslem... any soul that seeks God will not be confounded. You judge the exterior. God judges the interior. God looks at the heart.

You perfectly exemplify where a BOD ultimately *always* leads, namely, to even ignorant infidels and pygmies in heaven. Never mind Scripture teaches that to not believe in Christ is a sin, and that to die in that sin condemns them to hell.

In St. Thomas' Catechetical Instruction, he knows nothing of a BOD or of a BOB, he teaches:
"The Nature and Effects of Faith.--The first thing that is necessary for every Christian is faith, without which no one is truly called a faithful Christian.
[1] Faith brings about four good effects. The first is that through faith the soul is united to God, and by it there is between the soul and God a union akin to marriage. "I will espouse thee in faith."
[2] When a man is baptised the first question that is asked him is: "Do you believe in God?"
[3] This is because Baptism is the first Sacrament of faith. Hence, the Lord said: "He that believeth and is baptised shall be saved."
[4] Baptism without faith is of no value. Indeed, it must be known that no one is acceptable before God unless he have faith. "Without faith it is impossible to please God."[5] St. Augustine explains these words of St.Paul, "All that is not of faith is sin,"[6] in this way: "Where there is no knowledge of the eternal and unchanging Truth, virtue even in the midst of the best moral life is false."

But BODers say the 'desire' for baptism without faith, is of such immeasurably high value that it is all but a dogmatic fact that it saves. The whole idea is altogether absurd.

You perfectly exemplify where a BOD ultimately *always* leads, namely, to even ignorant infidels and pygmies in heaven. Never mind Scripture teaches that to not believe in Christ is a sin, and that to die in that sin condemns them to hell.

In St. Thomas' Catechetical Instruction, he knows nothing of a BOD or of a BOB, he teaches:
"The Nature and Effects of Faith.--The first thing that is necessary for every Christian is faith, without which no one is truly called a faithful Christian.
[1] Faith brings about four good effects. The first is that through faith the soul is united to God, and by it there is between the soul and God a union akin to marriage. "I will espouse thee in faith."
[2] When a man is baptised the first question that is asked him is: "Do you believe in God?"
[3] This is because Baptism is the first Sacrament of faith. Hence, the Lord said: "He that believeth and is baptised shall be saved."
[4] Baptism without faith is of no value. Indeed, it must be known that no one is acceptable before God unless he have faith. "Without faith it is impossible to please God."[5] St. Augustine explains these words of St.Paul, "All that is not of faith is sin,"[6] in this way: "Where there is no knowledge of the eternal and unchanging Truth, virtue even in the midst of the best moral life is false."

But BODers say the 'desire' for baptism without faith, is of such immeasurably high value that it is all but a dogmatic fact that it saves. The whole idea is altogether absurd.

If St Thomas knows nothing of BOD or BOB in his "Catechetical Instruction", he clearly teaches it in the Summa, did you not read my earlier post? 

No, I do not hold that someone can have BOD without faith. But I do hold as absolutely certain that God desires every man to be saved, and that he gives every man the grace to save his soul. The conclusion is obvious. God is not limited by the ordinary means He established for salvation, He sees the heart, and the Almighty acts directly on souls. Faith usually comes by hearing, yes, that is the ordinary way, but with some, it is clearly impossible. Were they then created for damnation? Just a simple yes or no will do.