2) National organisation, local church leadership. Each "franchise" of a parachurch is responsible to one particular local church. Thus, the staff workers in that "franchise" will be entirely accountible to the eldership of that one local church. This would be the model of Campus Outreach here in the USA. http://www.campusoutreach.org
I had the privilege of meeting with a team of Campus Outreach workers recently. One of my church's supported workers works with Campus Outreach (though we have/have had supported workers with Campus Crusade, IVF, IFES as well).
Quite apart from the particular structure that they advocated, I deeply appreciated their commitment to and passion for evangelism of students, but also to the local church.
The advantages of the model that they have include:
a) Clear accountibility of the leadership to a local church.
b) Ease of encouraging students who are being discipled into a local church.
c) the advantages of a national organisation in terms of resources, expertese (e.g. the organisation could provide wisdom on how to liaise with university officials as to how to have legit status on Campus)
d) An ethos that multiplies ministries nationwide and beyond - those who benefit from Campus Outreach may go and serve students on another campus.
The challenges I see for this model include.
a) having a close tie to a particular local church to which the staff workers are accountible raises the question of dual accountibility. There is accountibility to the local church, but also to the national organisation.
b) It would have most of the same problems as the 'Local church only' model in terms of united witness. I assume if the partner church is First baptist, they won't usually have one of the pastors of Second Presbyterian speaking at the main meeting.
c) It may cause problems of conscience for some of the staff workers. They might be convinced presbyterians, but the partner church is a baptist church. would they be obligated to go against their conscience over baptism?