Va. Code § 58.1-3807
When any county imposes the tax authorized by this article and there is located in such county a city having no separate court in whose clerk's office wills are admitted to probate or grants of administration are issued, the governing body of such county shall at least semiannually pay into the treasury of such city an amount equal to the county tax collected on the probate of wills or grants of administration for each decedent residing within the corporate limits of such city at the time of his death, less the proportionate compensation, if any, paid by the county to the clerk for the collection of such tax. The clerk of the court shall compile and furnish the necessary information to the governing body of the county to enable it to comply with this provision.
Va. Code § 58.1-3807