I've been seeing more and more of these scenes lately (though I know they aren't new), as they add shock value to a particular scene/story line. Just curious if it's split-scened or just a part of the job.
This can often come down to the willingness of the actors concerned as to whether to go all the way during a 'spitting' scene.
Sometimes you will indeed see the shot as an edited one - 'spitter' spits, cut to 'spitee' receiving the phlegm. This is easy to pull off and does not have to involve any real phlegm hitting the 'spitee's' face - this can be simulated with water/egg white/corn syrup.
However, when you see the shot as a two-shot (both actors in frame), then there is no faking it, but you can rest assured that plenty of mouthwash is involved, plus a similar mixture as described above to create the most effective spittle, a substance that will cling to the face but then also dribble in sticky strings.
I don't have any links to back this up, as I am going by my own filmmaking experience alone, but would welcome any edits to this answer if anyone has anything to add.