Aspects of the relationship:

Part of serial A separates to become serial B (C, etc.); serial A continues minus the part which is not B; (if serial A ceases use "split into" instead)

Linking entry fields:

Serial A: one or more fields tagged 785 X1; or when there are multiple titles combined into a 580 and code each field as 785 11

Serial B (C, etc.): one field tagged 780 07

See also:

14.2. Chronological relationships (fields 780/785)