Do you mean who exercises the OUM?

That is clearly defined by Vatican I.  Pope and the bishops teaching unanimously in union with him, when they teach something as being de fide, cannot err.

^^^^ Novus Ordo doctrine - see Lumen Gentium 25.

You see, when you miss and fail to articulate a necessary distinction, it always looks like you're contradicting yourself.  What they're all missing is the formal/material distinction originally articulated by St. Robert Bellarmine and masterfully applied to the current crisis by Bishop Guerard des Lauriers.

You see, when you miss and fail to articulate a necessary distinction, it always looks like you're contradicting yourself.  What they're all missing is the formal/material distinction originally articulated by St. Robert Bellarmine and masterfully applied to the current crisis by Bishop Guerard des Lauriers.

It is an unnecessary distinction or perhaps best left up to competent theologians to sort through some day.

The fact is, the hierarchy is not infallible, either in a council nor dispersed throughout the world - this idea is a major cause of confusion, particularly among sedes. Per V1, only the pope is infallible when he defines a doctrine ex cathedra.

Sedes believe LG 25 is a Church dogma - and it is a dogma - of the conciliar church, not the Catholic Church.They read "hierarchy" and "Magisterium" as one and the same, both infallible which is altogether wrong. So when they see the hierarchy spreading error, they say the infallible magisterium as defected - which is the completely wrong thinking inspired by the NO doctrine in LG 25. All it does is start debates about formal/material that has nothing to do with reality at all.  

It is an unnecessary distinction or perhaps best left up to competent theologians to sort through some day.

The fact is, the hierarchy is not infallible, either in a council nor dispersed throughout the world - this idea is a major cause of confusion, particularly among sedes. Per V1, only the pope is infallible when he defines a doctrine ex cathedra.

Sedes believe LG 25 is a Church dogma - and it is a dogma - of the conciliar church, not the Catholic Church.They read "hierarchy" and "Magisterium" as one and the same, both infallible which is altogether wrong. So when they see the hierarchy spreading error, they say the infallible magisterium as defected - which is the completely wrong thinking inspired by the NO doctrine in LG 25. All it does is start debates about formal/material that has nothing to do with reality at all.  

There is no such organisation as the "Conciliar Church". If Vatican 2 was a valid council, then the so-called "Conciliar Church" IS the Catholic Church. If the post-V2 Popes were valid, then their proclamations, decrees, promulgated rites, etc. were all done for the Catholic Church. It is ridiculous to assert that the Popes could've accidentally created a second Church that they didn't know existed and then accidentally only issued their decrees, etc. for the "Conciliar Church" which they didn't even know existed, despite each one explicitly referring to the Catholic Church and their authority as its leader. 

There is no such organisation as the "Conciliar Church". If Vatican 2 was a valid council, then the so-called "Conciliar Church" IS the Catholic Church. If the post-V2 Popes were valid, then their proclamations, decrees, promulgated rites, etc. were all done for the Catholic Church. It is ridiculous to assert that the Popes could've accidentally created a second Church that they didn't know existed and then accidentally only issued their decrees, etc. for the "Conciliar Church" which they didn't even know existed, despite each one explicitly referring to the Catholic Church and their authority as its leader.

Oh, the conciliar church certainly does exist, as Fr. Wathen puts it in his book, Who Shall Ascend?:

....The reader is implored to believe that as it is in the spirit of Christian charity that we have been compelled to proclaim the Catholic Church to be the sole and exclusive instrument of salvation for men on earth, it is in the same spirit that we assert the major thesis of this third part, viz., the Conciliar Church is not the Catholic Church, though it is within it, like a fifth column.....

It's worthy to note, that Fr. Wathen is actually only saying that which has previously been said by Pope St. Pius X, below in the pope's teaching from Pascendi Dominici Gregis, the only real difference is that today, they are no longer hid, but they are still   within:

Gravity of the Situation

2. That We make no delay in this matter is rendered necessary especially by the fact that the partisans of error are to be sought not only among the Church's open enemies; they lie hid, a thing to be deeply deplored and feared, in her very bosom and heart, and are the more mischievous, the less conspicuously they appear. We allude, Venerable Brethren, to many who belong to the Catholic laity, nay, and this is far more lamentable, to the ranks of the priesthood itself, who, feigning a love for the Church, lacking the firm protection of philosophy and theology, nay more, thoroughly imbued with the poisonous doctrines taught by the enemies of the Church, and lost to all sense of modesty, vaunt themselves as reformers of the Church; and, forming more boldly into line of attack, assail all that is most sacred in the work of Christ, not sparing even the person of the Divine Redeemer, whom, with sacrilegious daring, they reduce to a simple, mere man.....

Sure, one can use the term "Conciliar Church" loosely, but the question is:  What is it?

Father Wathen agrees that whatever it is, it isn't the Catholic Church.

That's correct. And it is the new church with all it's new doctrines that arose from it's "new Pentecost" (V2) we see that have taken over the Catholic Churches nearly everywhere in the world.

In Pascendi, the pope warns they are hidden within the Church and as such, are all the more dangerous. One might think after reading that snip, that now that they are out in the open and are literally everywhere that they'd be somehow less dangerous, but the people followed the "infallible magisterium" - and even after 60 years of their abominations, still do.....because they believe LG 25, that whatever the pope/hierarchy teach, no matter how anti-Catholic, is infallible.

Your poll choices demonstrate that you not only know nothing about the OUM and what it actually is, but also that you lack any understanding of the current crisis.  You believe that the mere existence of the OUM is all that matters, even if it has defected from teaching truth.

You have it exactly right.  XavierSem craftily edited W&S to hide the part that completely destroys his own position.

Art II. The Indefectibility of the Teaching Body is at the same time a condition and a consequence of the Indefectibility of the Church. A distinction must, however, be drawn between the Indefectibilty of the Head and the Indefectibility of the subordinate members. The individual who is the Head may die, but the authority of the Head does not die with him --- it is transmitted to his successor. On the other hand, the Teaching Body as a whole could not die or fail without irreparably destroying the continuity of authentic testimony. Again, the Pope's authority would not be injured if, when not exercising it (extra judicium), he professed a false doctrine, whereas the authenticity of the episcopal testimony would be destroyed if under any circuмstances the whole body fell into heresy.
(Wilhelm and Scannell, Vol 1, Book I, Part I, Ch II, Sect 14)

Also W&S have 2 definitions of Teaching Body.  One is the narrow sense meaning the ordinaries.  The other is a more general sense of the entire hierarchy consisting of all clerics.  They are using the general sense when discussing indefectibility.

Clemens Maria, you are mistaken. Those words you have bolded in, "On the other hand, the Teaching Body as a whole could not die or fail without irreparably destroying the continuity of authentic testimony." are clearly in the OP, as anyone can see. The part on the Pope dying is not the question here, though even it confirms that the Teaching Body cannot die. The question is on the Teaching Body.

I'm disappointed to see 5 people (poll result) have admitted to objective heresy. Teaching and Governing are merely aspects of the same Office. Without being appointed to Episcopal Office by the Pope, one cannot exercise Ordinary Jurisdiction or Ordinary teaching authority.

See the CE, for example: "It may be noted here that the Decree "Lamentabili sane", of 3 July, 1907, rejects (n. 52 sqq.) the doctrine that Christ did not desire to found a permanent, unchangeable Church endowed with authority. It is customary to speak of a threefold office of the Church: the office of teaching (prophetic office), the priestly office, and the pastoral office (governing office), also, therefore, of the threefold authority of the Church, that is, the teaching authority, ministerial authority, and ruling authority. Since, however, the teaching of the Church is authoritative, the teaching authority is traditionally included in the ruling authority; regularly, therefore, only the ministerial authority and the ruling authority are distinguished. By ministerial authority, which is conferred by an act of consecration, is meant the inward, and, because of its indelible character, permanent capacity to perform acts by which Divine grace is transmitted. By ruling authority, which is conferred by the Church (missio canonica, canonical mission), is understood the authority to guide and rule the Church of God." http://www.newadvent.org/cathen/08567a.htm It would be just as heretical to say Teaching Authority  can cease to exist in the Church as to say that Ruling or Governing Authority, i.e. Ordinary Jurisdiction conferred by the missio canonica, can cease to exist in the Church. Both are impossible, and the defense of either proposition as possible, is objectively heretical.

Just to give a few examples of orthodox Catholic Bishops or Cardinals who without doubt are legitimate Ordinaries, Cardinal Burke, Cardinal Sarah, Cardinal Ranjith, and say, Bishop Tobin (there was great news about the TLM returning to a parish in his diocese the other day, and the parish being saved from closure through the TLM! - see the other thread for that) who has promoted the TLM are some. I'm sure there are others.

There are 5350+ Ordinaries in the Catholic Church. It is among them, the diocesan Bishops, (not necessarily all) that the OUM of the Church continues. It cannot be any other way. To exercise Teaching Authority, as the CE plainly says, missio canonica is necessary. 

Please read the CE carefully, especially this part (1) "the teaching authority is traditionally included in the ruling authority" (2) "By ruling authority, which is conferred by the Church (missio canonica, canonical mission), is understood the authority to guide and rule the Church of God."