When application deadlines are approaching, people always send questions about when the schools they selected will get their TOEFL scores.
The answer is not exactly clear. ETS says a few things.
On this page, they say:
Score reports are sent to your designated score recipients approximately 8–16 days after your test date.
On this page, they say that it depends on the system used by the school:
ETS® Data Manager: 6–8 business days
Scorelink® Service: 8–10 business days
And, finally, in the most recent TOEFL Bulletin, they say:
Official score reports for the TOEFL iBT test will be sent to your designated recipients within 11 business days after your test.
I suppose this means they could arrive as long as 16 days after you take the test. That seems to be the longest possible wait mentioned by ETS. If you are on a tight deadline, keep that in mind. They could get sent sooner than that, but don’t count on it.
Note, also, that scores for tests taken at a test center are reported to students more quickly than tests taken at home. It could be true that schools get those scores more quickly as well.