“I know that is the case. No assuming required.”
Merely a sad statement of faith, a presumption you take for granted, to which the facts do not agree.
Since you quoted Ignatius Theophorus, let me quote him for you:
See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid.
Letter to the Smyrneans, 8
For, since you are subject to the bishop as to Jesus Christ, you appear to me to live not after the manner of men, but according to Jesus Christ, who died for us, in order, by believing in His death, you may escape from death. It is therefore necessary that, as you indeed do, so without the bishop you should do nothing, but should also be subject to the presbytery, as to the apostle of Jesus Christ, who is our hope, in whom, if we live, we shall [at last] be found. It is fitting also that the deacons, as being [the ministers] of the mysteries of Jesus Christ, should in every respect be pleasing to all. For they are not ministers of meat and drink, but servants of the Church of God. They are bound, therefore, to avoid all grounds of accusation [against them], as they would do fire.
In like manner, let all reverence the deacons as an appointment of Jesus Christ, and the bishop as Jesus Christ, who is the Son of the Father, and the presbyters as the sanhedrim of God, and assembly of the apostles. Apart from these, there is no Church. Concerning all this, I am persuaded that you are of the same opinion. For I have received the manifestation of your love, and still have it with me, in your bishop, whose very appearance is highly instructive, and his meekness of itself a power; whom I imagine even the ungodly must reverence, seeing they are also pleased that I do not spare myself. But shall I, when permitted to write on this point, reach such a height of self-esteem, that though being a condemned man, I should issue commands to you as if I were an apostle?To the Trallians, 2-3
Since therefore I have, in the persons before mentioned, beheld the whole multitude of you in faith and love, I exhort you to study to do all things with a divine harmony, while your bishop presides in the place of God, and your presbyters in the place of the assembly of the apostles, along with your deacons, who are most dear to me, and are entrusted with the ministry of Jesus Christ, who was with the Father before the beginning of time, and in the end was revealed. Do all then, imitating the same divine conduct, pay respect to one another, and let no one look upon his neighbour after the flesh, but continually love each other in Jesus Christ. Let nothing exist among you that may divide you; but be united with your bishop, and those that preside over you, as a type and evidence of your immortality.
As therefore the Lord did nothing without the Father, being united to Him, neither by Himself nor by the apostles, so neither do anything without the bishop and presbyters. Neither endeavour that anything appear reasonable and proper to yourselves apart; but being come together into the same place, let there be one prayer, one supplication, one mind, one hope, in love and in joy undefiled. There is one Jesus Christ, than whom nothing is more excellent. Therefore run together as into one temple of God, as to one altar, as to one Jesus Christ, who came forth from one Father, and is with and has gone to one.
To the Magnesians, 6-7
Sounds sort-of, kind-of like the structure of the particular Church (a/k/a a diocese) to me.
Now as for the relations between Particular Churches, we have the following:
The bishops are not to go beyond their dioceses to churches lying outside of their bounds, nor bring confusion on the churches; but let the Bishop of Alexandria, according to the canons, alone administer the affairs of Egypt; and let the bishops of the East manage the East alone, the privileges of the Church in Antioch, which are mentioned in the canons of Nice, being preserved; and let the bishops of the Asian Diocese administer the Asian affairs only; and the Pontic bishops only Pontic matters; and the Thracian bishops only Thracian affairs. And let not bishops go beyond their dioceses for ordination or any other ecclesiastical ministrations, unless they be invited. And the aforesaid canon concerning dioceses being observed, it is evident that the synod of every province will administer the affairs of that particular province as was decreed at Nice. But the Churches of God in heathen nations must be governed according to the custom which has prevailed from the times of the Fathers.
First Council of Constantinople, Canon 2
While these days: Can. 390 A diocesan bishop can perform pontifical functions in his entire diocese but not outside his own diocese without the express, or at least reasonably presumed, consent of the local ordinary.
to which the facts do not agree.
OK, whatever.