A - Thanks for the question. Normally I answer the questions in full, but for this one, I am going to give highlights. For a more complete description (although somewhat dated) I will point you to the entry at the Catholic encyclopedia. It has more information about this subject than you will ever need.
An auxiliary bishop is an assistant to the bishop or archbishop in a particular (arch)diocese. They are appointed when the (arch)Bishop cannot oversee all they need to in their diocese. The auxiliaries have no authority outside of what the(arch)bishop gives them. This is because the real authority comes from being the bishop over the particular church (e.g., Austin, Dallas, San Antonio, etc.) and not solely from their ordination.
Now, because each bishop must necessarily have a diocese to oversee, the auxiliaries are given a see (aka - diocese) that is no longer occupied by the faithful or has been incorporated into another diocese. In other words, they are given authority over a former diocese that once existed, but no longer has anyone to oversee. This is called a titular diocese. Because there are no longer any faithful to oversee within the former diocese, the titular (arch)bishop has no actual authority over his titular diocese, but rather the Pope reserves that authority to himself.
You are correct that part of the reason for having auxiliaries is a matter of prudence. It costs more and stretches resources thinner the more dioceses you have. It also thins out human resources (priests, religious, and trained lay leaders). On the flip side, there is less personal contact with a (arch)bishop of a larger (arch)diocese.
There are new dioceses that are created, but it takes extraordinary circumstances to warrant it now. Remember that in Texas we have some very young dioceses. For instance, here are the dates for incorporating new dioceses:
- Galveston Houston was raised to an archdiocese in 2004
- Laredo was established in 2000
- Tyler was established in 1986
- Lubbock was established in 1983
- Victoria was established in 1982