Keeping >=80% of the spin-off is desirable for tax reasons. (It makes dividends from the spun-off subsidiary to the parent company non-taxable.)
PFE eventually divested all of ZTS via a stock swap where investors could exchange their shares of PFE for shares of ZTS in a tax-free transaction. For PFE, this transaction was tantamount to selling ZTS outright and using the proceeds to repurchase PFE shares—without the capital-gains tax that an actual ZTS sale would have incurred.
“The efficient-market hypothesis may be the foremost piece of B.S. ever promulgated in any area of human knowledge!”