Step 1: Goodwill Upon Admission When a new partner joins, existing goodwill on the books is written off. This process redistributes the prior goodwill among the existing partners. Step 2: Allocation Ratio The goodwill to be written off is distributed to the old partners based on their original profit-sharing ratio, which predates the new partner's entry. Step 3: Rationale This write-off prevents the incoming partner from gaining value from goodwill generated before their admission. Step 4: Summary Consequently, existing goodwill is eliminated among the original partners using their initial profit-sharing ratio.