In the US, primaries for the presidential election of the two major parties are usually funded and regulated by the state government. Is this also true for the smaller parties? In that case how is it decided what qualifies as a political party that can request a primary election?
Third-party primaries are generally funded by the parties themselves, as is the caucus and convention process prior to, or in lieu of, a primary, in the two major political parties.
Typically, however, the third-party nomination process is also more of a caucus and convention process than it is a state run political primary process. Often, third-parties don't even have a public primary process open to all voters affiliated with them as a matter of course.