Hi Readingveracal, and welcome!
Children living in Buckinghamshire who pass the 11+ seem to be guaranteed a place at one or other of the grammar schools. But what about the children who live "in catchment" but out-of-county (e.g. North Maidenhead)? Presumably they are not guaranteed a place at the Buckinghamshire grammars? Or are they?
There are no absolute guarantees of places for any child, regardless of which county they live in. In practice, however, children living in Buckinghamshire invariably gain places at a GS somewhere in the county.
it would be illegal to discriminate against children because they live in the wrong county (the Greenwich Judgement of 1989), but under the Rotherham Judgment 1997, schools may give priority to children within a defined catchment area.
So, provided you move to within the catchment area for a Bucks grammar school, regardless of which county you are in your application would be considered equally with those of children applying from within the county. Catchment children are currently the first priority after exceptional cases for all Bucks GS.
Whether your children then gain places is down to distance from school gates. If you take a look here you will see the sort of distances that have applied in recent years for schools such as Sir William Borlase, but please do read the update at the top about distance measurement: http://www.elevenplusexams.co.uk/school ... n-profiles
That is a starter for ten - hope it helps.