I have recently formed a new staffing company.

I have couple of questions
1) How to work as a 3rd party staffing company and make sure that we are not kicked off.
For Eg.
Let say there is an opening in company 'A' . Ompany 'A' contacted a staffing company 'B' to fill this position. 'B' then advertise this position in one of the job portals.Company 'c' looks this advertisement and searches for the right candidate.
The Candidate is an employee of another staffing company (lets say'D') .
Q) How should 'C' work to make sure that they are not kicked off in the process and 'B' and 'D' join hand togther.

When 'C' contact the candidate , he/she asks about the client .'C' cannot reveal the clients name. But candidate says that he/she wants to know as they want to make sure whether they have already applied for the client or not?

When 'C' contact 'B' , 'B' is asking for the contact information of the candidate as 'B' has to give it to their client, so that an interview can be scheduled.

HOW TO MAKE SURE THAT 'C' IS NOT KICKED OFF?

There are quite a few ways to do this...
1) make sure the salary to the employee is routed through you. The employer pays you and you inturn pay the employee (without taking a part of the sal)
2) The most common way to do it is, even before you give your employee details to the company, you come to an agreement with them stating that any reference of your they hire, they are liable to pay you for that. Eg: You give them a reference of candidates a,b and c & send them over for interviews... later you find out that employee b has been hiried, since you have it in black and white (through mail or whatever) that you sent him there, technically he is your reference and the employee needs to pay you the cut. This method is pretty common.

Of course if the employee quits within a few weeks or months (Agreed upon time) you have to replace him and can't be charging for the replacement.

There are a lof of ways this is done... what I've mentioned are the simplest and the most common way of doing it.