How do I treat goodwill when a new partner is admitted?

When a new partner is admitted, goodwill compensates the old partners for the share of profit they sacrifice. The modern treatment (as per AS 26) is that purchased goodwill brought in by the new partner is shared among old partners in their sacrificing ratio, not recorded as a permanent asset. If the new partner brings their share of goodwill in cash (premium for goodwill), you debit Cash and credit Premium for Goodwill, then distribute it to old partners in their sacrificing ratio by debiting Premium and crediting their capital accounts. If goodwill is not brought in cash, the new partner's capital account is debited for their share and old partners' capitals credited in sacrificing ratio. Sacrificing ratio equals old ratio minus new ratio. Only existing goodwill already in the books is written off first among old partners in the old ratio.