I would like to apply for a job which was posted online. After research, I found out that the exact same job is posted by different recruiting agencies (at least 12 oe more). Do I look for the most reliable one and apply only once (considering that they might not be the best choice and I will be sorted out), or do I send out my resume to all of them (considering that the company will sort me out because they have the same application 12 times). I was not able to find the employer.
Do NOT apply through multiple recruiters. Agreements with recruiters often include that they are the only one allowed to represent you to a given company (meaning you can't apply directly either). Going through multiple recruiters for the same company is viewed as a breech of ethics by many people. If a company gets your resume through multiple sources, they are much more likely to simply throw you out as untrustworthy or not worth the risk of a lawsuit with the competing recruiters.
You might find this question interesting as an example of what can happen when you go through multiple recruiters.
I would not apply to all of them. In my opinion, the company would get extremely suspicious if they saw your resume applying for the same job 12 times. If they were interested in you to start with, seeing this behavior may cause them to reconsider asking you for an interview. Furthermore, some recruitment agencies will ask that you only work through them--whether or not you're willing to comply with this is up to you, of course.
At best, you still get an interview and nobody notices/cares. At worst, they eliminate you as a candidate entirely, possibly burning bridges in the process. The risk isn't worth the gain, in my opinion. If you're qualified, one application should be sufficient.
In my experience, the process works like this. Applying through a recruiter does not mean your resume will automatically be forwarded to the hiring company. If the recruiter thinks you are a suitable candidate they will then ask if you will agree for them to represent you exclusively and then put your resume forward. It's possible that you apply through one recruiter and they don't think you are suitable but another recruiter does. I wouldn't apply to 12 recruiters but let's say you apply for the same job through three recruiters. One doesn't think you are suitable but two do and ask if you will give them exclusive rights to represent you for this job. You then have a choice to make and the hiring company will only be getting one resume from you, through the recruiter you have chosen to represent you for this job.