In the cases I have worked with a recruiter, both myself and the recruiter went over the rules beforehand. In my case, every time, the recruiter brought this up before I did, and I would normally think this would be standard practice by them to protect their own interests.
Each recruiter I have talked with had their own rules. Some worked only with a group of companies they had agreed to rates with and relatively limited access to a list of positions with. If I wanted in to those companies, there were sets of positions that were only hired through recruiters, and they were one of a limited number of recruiters who could present for them, but they did not shotgun resume's to other organizations. That made it a no contests, I could not claim I found the position on my own, get the position, they were owed the commission. Others would search for me with their contacts. These were the ones that could result in fights.
Terms I would agree to were that I had to tell them where I had already contacted, and for a period of time they would not contact those places and I was on my own with them. Before they would present me information anywhere, they needed to tell me where that was and I would approve or decline. If I approved, then for a period of time, typically 6 months, any position I accepted with that company would be considered their find, even if I felt it was not the position they put me up for. Thus, they would not try to steal commission for positions I found on my own, and I would not try to undercut them on their finds. It was not perfect, but resulted in no squabbles for me. But I would highly recommend making sure you and the recruiter understand each other and are not double working the same organizations.
When I worked with recruiters I did actually have to sign a contract with them, and I would really recommend this being in writing. I have known people who ended up in lengthy battles because they did not fully understand the rules and were working with firms who expected to be paid, and if the company did not agree to pay, the client was on the hook for the fee. A good friend could not take a position he wanted because he had sent a resume/CV in, and then the recruiter contacted the company. The company said they directly offered, would not pay, so the recruited demanded half a years salary from the applicant. He ended up still hiring with the company, but not until 6 months later and with a different position.