The rules state That an augmented rating may be no more than 1.5 times the natural maximum. (page 62). They also state (page 63) that for skills the maximum modified rating is 1.5 times the unmodified rating. The wording specifically describes the magical / cyber / adept bonuses to skills as giving extra dice.
A couple of questions as to what that means in specific cases:

With regard to skills, a specialization gives 2 extra dice. Does this count against the limit of .5 the base skill for bonuses? (If so, this seems to mean that you can not get full value for specialization unless you have a skill of at least 4.) This would be consistent as the only cyber bonus to skills is +1.
Is the adept skill bonus also listed this way?

If a spirit is aiding a mage in casting a spell, the "aid sorcery" power adds dice to the spellcasting or ritual spellcasting skill. Is this subject to the limit of 0.5 times the natural skill?

A Power focus adds dice to all uses of a mages magic attribute. Are these dice limited as an augmented rating for an attribute? If so, presumably the limit for magic + power focus use is 1.5 time 6 + initiation (assuming no reduction in magic from cyber?)

Yours,
Joel M. Halpern

The general consensus seems to be that these limits effect almost nothing. I'd recommend checking out the thread
[Attributes and Skill caps with 1.3 erratta] and posting further questions there rather than splitting this topic up too much.

If I understand the current rules / interperitation the answers to your specific questions are "no, those things are bonus pool dice and don't add directly the the skill".

Thanks. I had not been able to find that thread for some reason.
It does seem from that discussion that the consensus is that the limits on skills are almost completely irrelevant.

Yours,
Joel

This is addressed in the most recent erratta, which you can download from srrpg.com.
I believe the skill caps only affect Improved Ability (and maybe one or two other adept powers), and reflex recorders.