It's all done by computer and, presumably by complicated software, but be assured that it does work
I did ask how the software worked - for the algolrhythm - but no-one at Shire Hall could tell me that; they just buy the software in from Capita, I think. I wasn't being suspicious, and I've never seen any evidence that it doesn't work correctly - I was just curious.
The software will start by allocating any 'looked after' children who have passed for an 11+ school with a place at their 1st preference. It will then start with the child/children with the highest 11+ score and allocate them their 1st preference., then work down the children giving them their 1st choice unless the schools are by that point full with 1st choices with scores higher than your child - at which point the 1st preference disappears and your 2nd preference pops to the top of your list.
If, after looking round the schools, you think that - say - Ribston would suit your daughter better than HSFG, then make that your first choice. All the grammar schools are good, all cope well with bright and very bright children, so it really comes down to which school will suit your daughter best.
Glad I don't have to worry about it any more