I would think that the escrow company can do this if it's related to an open escrow and title insurance is purchased. I have never heard of a title company handling transfers of title without the purchase of a title insurance policy since the escrow services are typically just ancillary to the title insurance business. If title insurance is not involved, the only thing the escrow company would do is prepare the deed, notarize the signatures and handle the recording. Like I said, I have never heard of that being done, but would be curious to know whether the escrow department would handle it. I know that they do when someone buys without an agent from a FSBO. If they don't, I would hire a real estate attorney to prepare the deed. The county office will not prepare it for them as that would be like giving legal advice. The county will only record the deed that's already prepared.
As the others have already mentioned, I would also want to make sure that the parents and children receive proper advice concerning any legal consequences of the transfer of title. It would probably also be a good idea to have the property appraised just prior to the transfer just in case the value of the property at the time of the transfer should ever become an issue. I hope this helps. Let us know what you find out from the title/escrow company.