As a rule, no subordinate character is ever run by the player running the lead character. Familiars, Shield Grogs, Custos, Apprentices- if they are significant, they should be individuals, and never just a convenient extension of the player's "main" character. (Some players can do this, even to creating conflict between the two- but even then, it's "better" to allow another player the opportunity to play, if at all possible.)
I'd say that the Player of the Parens planning to eventually play the apprentice and retire their current mage is a bad call, but that's just my opinion. It could certainly work, but for me it's a munchy way around the rules, ignoring any current story and focusing on the future numbers.
As far as a Parens grooming an apprentice to be an uber-mage?... well, you have to ask yourself, your Story Guide, your Troupe- is Game Balance important? The same could be done with any character started at a young age, to become a shield-grog from hell, or at least something far more than the RAW allow.
Far more than many RPG's, Ars Magica isn't a game as much as the story that game gives us. Players who are looking for a system to abuse should be disappointed, and easily can be by a wise and judicious SG. If the parens seems to be spending 3+ seasons/year training his apprentice, ignoring all else, then it's up to the SG to provide that mage character with something else to think about- he owes it to the player. 
However, if you wanted "rules" (bleh), I'd say that as far as adventure XP, the apprentice would get half, at most- the rationale being that children don't make their own decisions as much as follow orders. Also the fact that the apprentice will be protected much of the time, and just not be "in the mix" as much.
As far as training, sketch out the finished apprentice at Gauntlet, and then work backwards, and balance any RP'd advantages just as if you were to build the character, with Virtues/Flaws. Maybe not a full +10/-10 with mathematical precision, but "close enough" should be the goal. The final Mage character should be "more or less" as balanced as he can be.
If he has extensive training, then the Virtues of "Skilled Parens" and perhaps "Priveleged Upbringing" would be required in the final product, since those are, in fact, exactly the benefits that the apprentice is enjoying. If given a formal, focused education in Latin, then that is close enough to a grammar school education to justify "Educated". If given an unusual or rare schooling, then "Student of (Realm)", "Well-Traveled", or even "Warrior" are justified to be required Virtues - they would be for any other character, right?
(If your apprentice already has +10 Virtues, and these are known to the Parens, then the SG has already made a blunder, imo, both for tying him down and showing his hand. I'd suggest he go back and change some as necessary, as children often don't evidence all the advantages that an adult does. Otoh, he could add extra Flaws via storylines, or even have existing Virtues "destroyed" by exceptional events - that can work too.)
Just as a 20 year old mage, who is then RP'd thru 20 years, will be larger than that same mage "CharGen'd" to age 40 initially, your apprentice will be larger. How much? "Some". "A reasonable amount". Whatever is acceptable to your SG and your Troupe.
But if, after buying all these educational bonuses and then using a fudge factor, you find you have nothing left for Hermetic Virtues and other desired aspects... gee, that's too bad. Good thing he had a great learning environment, huh?