Out here in New York City, where the barbarians are savages, the mongrels will just whip it out and piss wherever. The kind ones will at least go to a far corner, some may even do it into a bottle of some sort...But most, especially late at night...Right on the floor.
The best tactic in this day and age is to take a cell phone photo (the face! sickos!) and call the police, the newspaper prints perverts pics (The NY Post is guilty)