What is the primary difference between: (i) accounting for a business combination when the subsidiary is dissolved; and (ii) accounting for a business combination when the subsidiary retains its incorporation?

It is not formally recorded in the accounting record of the parent company if the subsidiary retains its incorporation.

Explanation:

IFRS 3 explains business acquisition as the taking over the control of an existing business by another with the acquired assets measured at the fair value at the date of transaction.

The combining of interest method has ceased to be considered by GAAP since 2001.

That means a subsidiary has to lose its incorporation for full acquisition or rather treated as an investment by the acquiring company.