Does one usually get a notification of receipt of a PhD application? I sent a PhD application almost 3 weeks ago on a thursday afternoon. As it happened, the next friday was a holiday. Something I noticed after sending the application.

Does one get a notification of receipt after sending an application?

My fear is that I sent the e-mail on thursday, when the PI and professor were already out. That, together with the 3 day weekend, and the mountain of mails probably coming on monday, buried my application and it went unnoticed.
It really depends on the school, and the channel of communication. I usually follow up after a week of sending an email if I were applying to a specific professor.

Using the example of my school, PhD applications are handled centrally, and you only get an email of further inquiry or rejection.

In either case, there are probably a lot of applications that the professor needs to sort through, a smart follow up is usually necessary.