In our PTA, the president is also an ex-officio member of each committee. I think it depends on the style of the president as to how involved they are in each committee; hopefully, the committee chairs were carefully selected and they are dependable (ours have always been). Also, it depends on if you have a new committee chair, or someone that has been there before as to how involved you need to be.
If there are major questions about how something is done, or whether or not it should be done at all, or it involves additional money, resources, etc., then there is some discussion with the board, just to get a feel for direction.
Generally, we allow the committees to determine how they want to accomplish things, and then each committee chair presents a report to the board. We currently have 25+ people on our board, and only an hour for each board meeting, so it doesn't make sense to discuss everything at every meeting; we usually trust the committee chairs to take care of their responsibilities and manage their budgets.
I could not agree more with Daddio44. It is a business. You are responsible to run the business. I, also,am aware of everything going on. Ultimately, it does come down to you if something goes wrong. In our bylaws the co presidents are ex-oficio of all committees. I try not to micro manage, but if something is just not right, I will put my two cents in and sometimes I have had to change things.
Do people like this? Not all the time, no! And believe me, I hear the grapevine talk, about how many people don't care for me. (Most don't even know me, and I am a likable person, I can work with anyone. Sometimes that can get to you but you get over it) However, it is a responsibility that comes with the position.
According to our by-laws, it is not defined either. But, it does state the the president oversees the execution of all items. Ultimately, it is the problem of the board when something goes wrong, so they need their two cents.
I do not see my self as a dictator or anything like that, but I do have my hands in everything. I try to run the PTO like a business so I give the committees the flexibility they need, but do stay involved, flag concerns, etc. There is not much going on that I am not aware (some I agree with, some I don't, but if there is nothing wrong with it from an objective view, I leave it be.).
There are questions in my school's PTO about how the Committees function in relation to the PTO Board. One of the current Officers thinks that all Committee decisions need to be approved by the PTO Board. My view (as a fellow officer) is that the Committees are established so that the decision-making powers are delegated so that the PTO Board can deal with the "overall" PTO issues. Plus, if the PTO Board had to meet every time there was a decision to be made in each Committee, we'd constantly be in meetings. Just curious how other PTO's handle this.