Gezzill, tis a bit of a waiting game!
You will get a letter confirming PSA have received your file! The length of time it takes from assessment day to getting that letter varies, I had to wait almost 4 weeks. Others I know, it only took 2 weeks, depends how busy they are!
Once you do get that letter, they probably still have to process your file, which can take a week or two. But there is a phone number on the letter you can call, and once they have processed your file, they may let you know the competitiveness of it!
TR