Setting the Default Account Model to Household will allow the university to capture Contact's family information using Household Accounts, which are automatically created when new Contacts are added. Setting the Default Account Model to Administrative will create Administrative Accounts, which are used to group Contacts by their affiliation to an educational institution or organization, not by their family relationship. Populating the Account field with the Household record is not a valid action because the Account field is read-only and automatically populated based on the Default Account Model. Reference:
https://powerofus.force.com/s/article/EDA-Account-Model
https://powerofus.force.com/s/article/EDA-Accounts-and-Contacts