Schools
Some parishes have schools on their campuses. Most do not. I suspect these school are separate corporations from the parishes with separate sets of books. The money to run these schools comes primarily from tuition paid by parents. There are also contributions from the public and from the parish the school is associated with. Indeed, when a student’s family is a member of a different parish, there is sometimes a transfer of money from the student’s parish to the parish of the school he or she attends. The diocese essentially subsidizes these schools by reducing the Cathedraticum assessment. Parishes with schools pay an assessment to the diocese of 9% of revenues while parishes without schools pay 10%. Further the diocese expense statement shows an additional $900,000+ in money to schools but this number is pretty small compared to the total budget of the schools.
Elementary and middle schools (there are 17 in total) are on parish grounds, but high schools have their own campuses. Of the six Catholic high schools in the diocese, 5 appear to be controlled by the diocese while 1 is independent. By controlled, I mean the arrangement seems to be that of not-for-profit corporations with board members selected by the diocese.
The sole exception is St Michael’s Academy in Austin which is in the same situation as St. Edward’s University is. It owns itself and is run by a board of trustees. It is Catholic because it says it is Catholic. If the board of St. Michael’s voted to change affiliation to Episcopalian or Baptist tomorrow, there is nothing the diocese could do about it. The other five high schools are presumably under diocesan control to a greater extent, just as the parishes are. However, in matters of education, St Michael’s seems to recognize the authority of the Superintendent of Catholic Schools, who is appointed by the bishop.
How big is the local Catholic school system? Compared to the public schools system, trivially small. On the order of 1% of students in the area (of all faiths) attend Catholic schools. The percentages is higher for Catholic students, but still well under 10% Compared to the parishes and CAO, however, the school system is a pretty good size. There are over 500 teachers. Support staff might be shared between parishes and schools in some cases (the same maintenance guys service both.) If you added up all the non-school staff from all the parishes and the CAO, I would guess the total would be on the order of a thousand. So by this metric, the schools make up a sizeable chunk of what the local Church does.