Actually I think we have some crossed wires here !
There is no suggestion on the website that Childwall was split into four parishes in medieval times.
Two of the chapels mentioned are said to be 'chantry' chapels within the church. These functioned something like side chapels in a cathededral, ie. they are not separate churches or buildings at all. The idea of a chantry chapel in the medieval period was to provide somewhere for a priest to say a daily mass for the dead. Some family who had enough money could have a chapel constructed within the parish church and would also provide an income sufficient to maintain a priest for this purpose. This would usually be done by signing land over to the parish in question. The income derived from renting out the land was for the priest. This was what the Norris family, for example, would have done. The idea was that the priest would be praying for the deceased members of the Norris family.
Even having a separate chapel building does not automatically mean it constitutes a separate parish. Liverpool was all originally part of the parish of St. Mary's at Walton on the Hill. I believe St. Nicholas at the Pier Head was first built as a 'chapel of ease' for Liverpool people who, until then, were forced to travel all the way to Walton, which was their parish church, on Sundays and saints' feast days. At a later point when the population increased, St. Nicholas was made a parish. It's always been the church authorities that created a parish, not the fact that a chapel existed.
Sorry for the lecture. Medieval history is one of my interests.
Joney
