I have been working at FAPESP full-time (More than 3 years)
FAPESP provides the best (i.e. higher value) scholarship for PhD and MSc students in the state of Sao Paulo, Brazil.
Highly bureaucratic, demanding financial and scientific reports annually. However, this is typical for most research funding agencies.
I applied through other source. The process took 6+ months. I interviewed at FAPESP (Edinburgh, Scotland (UK)) in September 2008.
This is relatively simple: You should fill in all the docs on the website. But before, you should have found a laboratory, in SP, and you should convince the head of the lab to welcome you and your project.
In my case, it has been an informal interview, in person, during a congress (Sept 2007 not 2008).
As a post-doc, you have to write a project, which will go through several processes and several levels of assessments by professionals of the field.
Then, after 6-8 months, a formal answer will be given for a two-years contract (extensible for one more year but you have to go through the same process (a bit shorter, only 3 months, but the answer can be "no")).
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