Bit of a hypothetical.
When a mage is kicked out of their House, and declared Orbis, what happens to any Apprentice they are training?
The house keeps the Apprentice, or the Orbis mage?
If the Orbis mage keeps the apprentice, bur can't find a new House within a year, is the apprentice marched along with the parens, or does some other mage claim the apprentice because the apprentice hasn't received training for a year?
I would think the mage keeps the apprentice, until they are marched, at which point one of the mages who participated in the march claims the apprentice as spoils of the march. Unless of course a Bonisagus claims them to keep them out of harms way before the orbis mage is marched.
It would depend on SG fiat if the local or Grand Tribunal has ruled on this edge case in the past. Certainly what @silveroak says is true, so those are also possibilities. Another consideration is how many enemies the magus and said apprentice already have. Once cast out, both lose any kind of legal protection, some kind of Peripheral or Grand Tribunal ruling notwithstanding.
I really cannot see any argument to deprive the master of their apprentice. The magus swears the Oath to the Order and not to the House, and the House claiming the apprentice would be a violation by depriving them of their magical power. Only when the magus is cast out of the Order, is the apprentice up for grabs, but the House does not have the authority to cast anybody out of the Order.
However, once the magus is cast out of the Order, the Oath no longer applies. It is a fair expectation that one of the marcher magi get the apprentice as a reward, but if the march drags out in time, and particularly if the apprentice is not quickly found by quaesitores and marchers, there is no clear rule to stop any odd magus from picking the apprentice up. I could see the quaesitores moving in quickly to take the apprentice into custody and thus secure the loot for the marchers, but if they do not manage to do that before a year lapses without training, they have to fight the default rule that makes them anybody's claim.
In short, in the case of a march, the situation is chaotic. A lot depends on timing, where first come is first served. A lot depend on peripheral rulings and the local organisation of the quaesitores and how efficient they are in organising the chaos.
If you wanted to be extreme, becoming Orbis could mean you are dead to your (previos) House, so maybe they act according to any will left in the House records?
One can imagine such a House Oath being made over and above the Hermetic Oath, yes. However, this would be akin to the Tremere tradition of passing the Sigil to one's parens, and here we have a canon ruling. This is legit only as part as the universal right to appoint a proxy. It is valid as a custom, but not as a binding House Rule. A disagreeing magus may leave the House and regain his Sigil at any time. Anything else would violate the Code.
Thus, the practise you suggest is a violation of the Oath, and I cannot see a way around that. Maybe there is, but it takes a clever lawyer.
Of course I should addendum that if the house they left is carrying a grudge one of the members could declare wizard war during the year of orbis and take the apprentice as spoils during the conflict as well. I could especially see this being done if a bjorner apprentice has already attended the gathering of 12 years and gotten their heartbeast thus being a full mage in the eyes of the house but not the order.
If you don't fit into either Flambeau, Jerbiton or Tytalus, it's not like the standards of House Ex Miscellanea are exacting. Even House Criamon offers guest passes as a form of sanctuary. It's hard to be both kicked out of your House and not find another House within the year, before getting Marched first.
It is not as if anybody knows who the ex misc members are so if you say you are a member, nobody is likely to dispute that.
A fair number of magi likely don't know who the ex misc primus is...
A fair number of magi don't know who the Tytalus primus is - but for different reasons.
Presumably the reason rhe mage was made Orbis may influence whether they are offered sanctuary /another House membership. As well as personality and reputation.
Maybe, but what reasons are there?
I don't imagine that a House would expel anyone for a marchable offence.
And I don't imagine anything short of a marchable offence to make them unwelcome ex Miscellanea.
To me, the most plausible case would be a magus who consider ex Misc a disgrace and prefers the March.
Good question.
These may be due to internal politics. If there's a struggle and you come up on top, managing to expell your rival is a way to enact your revenge and make any comeback from them difficult without breaking the code.
These may be due to external politics. If you've been working against your house to further the agenda of another house (say, working as a bjornaer agent to further the cause of wilderism into house jerbiton), you haven't broken the code or such, but I can sure see you being expelled.
These may be out of sympathy. Like "We realize that you don't belong into this house and would be happier elsewhere, yet, out of loyalty/habit/whatever, you'll never leave on your own. So we expell you, so that you may find a better way". Actually, this is something I can see Criamon do.
These may be due to your reputation. If you haven't broken the code, but your name is so foul that it becomes a stain on the house, I can see you being expelled. For example, if you're a backstabbing, cheating, murderous coward, I can see the current Flambeau expelling you. Likewise, I can see the jerbiton expell you if you're giving them a bad name.
So, I'd say, anything not covered by the code, and not serious enough to warrant a wizard's war
What about saving face- you were part of Tremere and were caught spying (non magically) on Ex Miscelania to find out if their leadership was being infiltrated by diabolists and so you had to be expelled from the Tremere house to save face, but of course it leads others to suspect that you might have been expelled to be able to infiltrate another house.
This is exactly what the Criamon do when a Criamon Maga’s stigmata disappears due to them no longer believing in the search for the enigma. On the other hand, the House usually waits until the Gorgiastic maga has found a sponsor for the new house before legally expelling them.
The cast-out mage keeps the apprentice, unless they are later Marched due to the annual expiration. If the mage is Marched, the apprentice is available, subject to a lot of situational complications.
Apprentices are not magi, so they cannot be Marched.
An interesting wrinkle: what if the apprentice is suitable, by reasonable standards, to Gauntlet? Again, situational complications, but they could be interesting.
Further complications for the apprentice:
If of any of the True Lineages, they are likely to be taken in by one of the House, but they might be resentful. For a Magus Mercere's apprentice, the master's offense would have to be remarkable, as the House is also family, and the magi so few.
The Cult Houses are also likely to take in the apprentice directly, partly because they are liable to hold cult secrets. For Bjornaer apprentices, who else would take them?
The Society Houses might be less concerned, especially Ex Miscellanea.
It depends on when they are able to gauntlet and the situation. For example if a mage orbus from bjorner were to gauntlet his apprentice during the year of Orbis I'm sure the house would welcome the apprentice into the fold- indeed I can see this being the case with most houses. If not then the apprentices period of Orbus begins with his being gauntleted.
If the wizard guantlets his apprentice after having been marched then things get trickier, and it will likely come down to the tribunal whether to recognize the gauntleting or not, possibly involving some form of examination by a bonisagus or guernicus. The real sticky part of course is the oath which will likely need to be readministered, and if the semi-gauntleted magus has been taught parma...
I do not think it is as complicated as you suggest.
Firstly, gauntlet is a matter for the house. It is the Oath that is the concern of the Order and thus the tribunal.
As 5ed is written, Parma should be learnt immediately upon taking the Oath. Having trained for some time, the final key is released quickly. Thus the only real case here, is the apprentice who knows Parma. If they swore the Oath, they swore it to a non-member and not to the Order. For such a person, there are only two ways, the Oath or a March. To swear the Oath, they need to find a sponsor who can initiate them into their house, which may or may not require a new gauntlet, depending on the House. There is no case for making this substantially different from a hedge wizard joining the Order, except that the master Orbus' house may accept them even if they are not a societates.
A more interesting question is if the apprentice can be trusted. Normally, I would think it trivial to find a parens/sponsor to take the apprentice on for a short period to complete/validate the training and administer the gauntlet. However, what if the apprentice has been trained in the foul ways of their former master?
Guantlet is sort of between the house and the order both. For example a bjorner is considered a full magus by he house after they complete the gathering of 12 years and claim their heartbeast. But the order requires a 15 year apprenticeship (except Thebes) and a guantlet for the apprentice to prove themselves. Admittedly a Bjorner can give an exceptionally easy gauntlet as a matter of house tradition, but the gauntlet has to be passed before they swear the oath and learn Parma.
Of course one point I didn't think about or cover is if a marched wizard guantlet's their apprentice, signs a letter that they have passed their guantlet and sends them back to an unmarched member of the order to swear their oath. At that point it shouldn't be much different than a Tytalus who has killed their master, except that other houses will have far less experience in this sort of thing, and the orriginal house has to decide whether to accept the apprentice in their ranks, but not being legally a member of the order yet they would indeed be much like a hedge wizard at that point in terms of rights.