Edinburgh,
The issues are
a) population density
b) a culture (relatively modern) of 'moving to get into a good school'
Some years ago, local 'priority admissions areas' changed. At that point, they modelled that these areas were of the right size to produce around the right number of 11 year olds for each school.
The problem is that one of these schools is considered 'better' than the others, so families moved into its priority admissions area in large numbers. New houses were also built.
So 3-4 years down the line, far more 11 year olds lived in the priority admissions area as were initially modelled. Siblings within that area get priority. So about 100 11 year olds on the outer edges of the 'priority admissions area' [would be called catchment in Scotland] weren't allocated places in that school, because it couldn't suddenly magic up 4 extra forms of entry.
Meanwhile, across the town, 4 forms-worth of places in other schools would have remained unfilled if all 'catchment' children got a place at the desirable school.
This would rapidly snowball - the following year, knowing that 4 forms of entry DID get in, then 5 extra forms would be required due to even more families moving in etc etc.
Essentially, the Scottish system relies on a) slightly excess capacity (so a few more people applying in a given year CAN be accommodated) ab) lower population density and c) less high-stakes comparability (there may be an 'unofficial' pecking order of schools, but not the high stakes Ofsted-and-league-tables thing), which is what drives the flocking of parents to specific schools.