"
Or must all of the deduction be used by the estate's return?"
All of the deduction must be used on the estate's income tax return. The estate, itself, actually paid the tax and, with real estate taxes, the deduction accrues to the individual or entity in the year in which the tax is paid (not necessarily the same year the tax is due).
None of the property tax is allowable as a deduction on the decedent's final return because the decedent never actually paid the tax while he was alive.
See https://www.irs.gov/publications/p559/ar02.html#en_US_2016_publink100099616
