I came across the thread whilst researching my own History
having served Borstal training in the 1970's, to answer your question where you served your training wasn't related to where you came from. When sentenced to Borstal training you were sent to the local Borstal allocation centre, this locally would be either Walton or Strangeways. In my case I went to Strangeways, there you would be assessed as to which Borstal would be best for you. Well that is what they tell you anyway. Borstal training was from six months to two years, wherever you went had different criteria for your earliest release.
You were allocated to a Borstal depending on what you were sentenced for, and your own record whilst in any previous institutions, and whatever training they thought you required.
You would be sent to an open, semi open, or a closed Borstal usually you served longer at an open, less at a semi open and the shortest at a closed. I spent two months at Strangeways before being allocated this counted towards the 2 years maximum but didn't count from your earliest release.
On the day I was moved there were 5 others moving, me and another lad from Birkenhead went to Hindley a closed Borstal our earliest release was the 1st, 2nd, or 3rd Thursday 9 months from the date you entered depending on your behavior. Two from Liverpool went to Wetherby which was 15 Months minimum, another two one from Liverpool and one from Wallasey went to Hatfield which was 18 month minimum. They did try and keep you as local as possible not for your sake but for your family who had to do any travelling to visit you.
One problem I have found whilst researching is a lot of stuff is sealed for 75 and 100 years, especially places that held juveniles so getting facts is difficult, even regarding yourself. Even if you can get it it is not always useful I received some stuff from my time in care that was so redacted it wasn't worth reading.