How to verify authenticity of submitted assignments When teaching 250 students in the same subject, knowing each student can be quite difficult. In smaller classes, it may be possible to learn enough through classroom interaction that when assessing the assignments it may be easy to tell if it is their work or not. For example, if a student can never form a coherent argument when asked in class, but that same student submits extremely high quality work, the teacher might want to dig a little deeper to see if the student is just better at writing or if they are hiring a ghost writer to produce their reports for them. However, in large classes, there is too little interaction with each student to form a strong opinion of everyone. Those who can 'hide' in class are the least likely to be 'caught.'

I see one option as incorporating an oral exam into the overall mark and using that mark as a basis from which to judge the student's future work. It's not perfect but it's something. One problem is that with 250 students, oral exams end up consuming so much class time that little time remains for lectures.

Running through something like TurnInIt will only catch if they are taking from an existing work but it will clearly not catch ghost writing.

What are the most effective ways of verifying authenticity of student assignments?
I'm going to give you an answer you may not want to hear: it isn't worth it for a class that big.

The pedagogue in me doesn't like my own answer, but as they say, you have to choose your battles, and I believe there are more important issues when teaching a class that large than to worry about catching the homework cheaters. Mitigation can include reducing the impact that homework has on the overall grade (but this leads to other issues, such as students wondering why homework is necessary if it isn't worth much in the final grade).
Another (probably less successful) method is to instill the fear of [insert deity of choice] into your students when it comes to cheating. If you do catch a cheater, make an example of that person that the other students won't forget -- I threaten to fail any cheater instantly if I can prove they cheated in any way, and I say it as matter-of-factly as I can on the first day of class: "Look, if I catch you cheating, I'll fail you, end of story."

If you have a balanced set of assignments that includes in-class exams, then poor performance on exams should produce final grades that indicate that the student hasn't learned the material.

If you can work out the oral exam, that might help balance out any poor knowledge, but beware that some students are absolutely terrified of oral exams, and they might know the knowledge as well as anyone else on paper but not be able to perform out loud.

I suggest not losing sleep over a few cheaters in a class that big, and to ensure that you're giving good assignments that are challenging and provide a good means for learning the material.