Thank you, Colleen.
I have done further research on this issue and have spoken to your tax colleagues at Turbotax. Where a payroll service collects and remits income and social security taxes on behalf of an employer of domestic employees, especially where that employer's payroll taxes are remitted through his separate household employer taxpayer identification number by the payroll company, no form H needs to be filed with the employer's 1040. To do so would result in double counting the taxes due to the IRS.
Similarly, as a separate tax identification number for the payroll taxes is used, trying to include the payroll taxes paid by the payroll company on the estimated payments section of the employer's form 1040 would result in incorrect estimated tax payment information on the employer's 1040. This is certain to trigger a payment error on the IRS's computer and repeated enquiries and audits from the IRS.
