Associating polygons with overlapping polygons by area of overlap (known as allocation factor)

I am attempting to associate School Attendance Boundary (SAB) polygons with Zip Code Tabulation Area (ZCTA) polygons. They are in separate .shp files.

One approach is to weight the allocation of a SAB to a ZCTA by the proportion of the SAB area that lays in the ZCTA area, i.e. if SAB_1 is 100ft^2 and 10ft^2 lay in ZCTA_1, then the allocation factor to be used in associating measures from SAB_1 to measures from ZCTA_1 is 0.1.

I note that these are common values for associating geographic areas (see MCDC Geocorr for examples). A previous Q&A (Calculating percentage of overlap between two different layers) provided a helpful walkthrough, but was not sufficiently detailed for me.

For example, one instruction was to "execute a union" and set a target layer. To my knowledge, unions don’t involve targets.

How can I obtain the allocation factors I have described?