Our school has capacity of about 100 pupils but normally has less than that. There isn't enough physical classrooms or children to have single primary classes, so do composites, with each composite having about 20-25 kids.
I believe you are correct in that you are guaranteed a place at either a catholic or non-denominational primary or high school based on your postcode, whichever you prefer.
You can also opt to make a placing request to any primary or high school outwith your catchment or council area and you have to hope there are places leftover in a school after catchment places have been fulfilled.
Places are then given out based on criteria first:
"The following criteria are then used in order to prioritise each group of applications:
1.Medical/ASN grounds relating to the child making the application, such that the chosen school is the only school that could provide for the child. These must be supported by documentary evidence from the family doctor and a local health practitioner. The Service Manager with responsibility for ASN will assess all applications seeking to receive recognition under this category.
2.An older brother or sister will be attending the same establishment for the session the application is being made.
3.The child is from a family that has exceptional family circumstances or is from a lone parent family. You may be asked to support this by suitable documentation."
And then finally any further leftover places will be given out to remaining placing requests, or rejected if no places left and you have to go to your catchment school.
I have a relative living near the city and they run 3 or 4 intakes of each primary year, they have the physical classrooms and student numbers so have no composite classes.