edit:
Here is the Ohio code
§ 4503.12. Transfer of ownership and registration.
(A) Upon the transfer of ownership of a motor vehicle, the registration of the motor vehicle expires, and the original owner immediately shall remove the license plates from the motor vehicle, except that:
(1) If a statutory merger or consolidation results in the transfer of ownership of a motor vehicle from a constituent corporation to the surviving corporation, or if the incorporation of a proprietorship or partnership results in the transfer of ownership of a motor vehicle from the proprietorship or partnership to the corporation, the registration shall be continued upon the filing by the surviving or new corporation, within thirty days of such transfer, of an application for an amended certificate of registration. Upon a proper filing, the registrar of motor vehicles shall issue an amended certificate of registration in the name of the new owner.
(2) If the death of the owner of a motor vehicle results in the transfer of ownership of the motor vehicle to the surviving spouse of the owner or if a motor vehicle is owned by two persons under joint ownership with right of survivorship established under section 2131.12 of the Revised Code and one of those persons dies, the registration shall be continued upon the filing by the survivor of an application for an amended certificate of registration. In relation to a motor vehicle that is owned by two persons under joint ownership with right of survivorship established under section 2131.12 of the Revised Code, the application shall be accompanied by a copy of the certificate of title that specifies that the vehicle is owned under joint ownership with right of survivorship. Upon a proper filing, the registrar shall issue an amended certificate of registration in the name of the survivor.
(3) If the death of the owner of a motor vehicle results in the transfer of ownership of the motor vehicle to a transfer-on-death beneficiary or beneficiaries designated under section 2131.13 of the Revised Code, the registration shall be continued upon the filing by the transfer-on-death beneficiary or beneficiaries of an application for an amended certificate of registration. The application shall be accompanied by a copy of the certificate of title that specifies that the owner of the motor vehicle has designated the motor vehicle in beneficiary form under section 2131.13 of the Revised Code. Upon a proper filing, the registrar shall issue an amended certificate of registration in the name of the transfer-on-death beneficiary or beneficiaries.
(4) If the original owner of a motor vehicle that has been transferred makes application for the registration of another motor vehicle at any time during the remainder of the registration period for which the transferred motor vehicle was registered, the owner may file an application for transfer of the registration and, where applicable, the license plates. The transfer of the registration and, where applicable, the license plates from the motor vehicle for which they originally were issued to a succeeding motor vehicle purchased by the same person in whose name the original registration and license plates were issued shall be done within a period not to exceed thirty days. During that thirty-day period, the license plates from the motor vehicle for which they originally were issued may be displayed on the succeeding motor vehicle, and the succeeding motor vehicle may be operated on the public roads and highways in this state.
At the time of application for transfer, the registrar shall compute and collect the amount of tax due on the succeeding motor vehicle, based upon the amount that would be due on a new registration as of the date on which the transfer is made less a credit for the unused portion of the original registration beginning on that date. If the credit exceeds the amount of tax due on the new registration, no refund shall be made. In computing the amount of tax due and credits to be allowed under this division, the provisions of division (B)(1)(a) and (b) of section 4503.11 of the Revised Code shall apply. As to passenger cars, noncommercial vehicles, motor homes, and motorcycles, transfers within or between these classes of motor vehicles only shall be allowed. If the succeeding motor vehicle is of a different class than the motor vehicle for which the registration originally was issued, new license plates also shall be issued upon the surrender of the license plates originally issued and payment of the fees provided in divisions © and (D) of section 4503.10 of the Revised Code.
(5) The owner of a commercial car having a gross vehicle weight or combined gross vehicle weight of more than ten thousand pounds may transfer the registration of that commercial car to another commercial car the owner owns without transferring ownership of the first commercial car. At any time during the remainder of the registration period for which the first commercial car was registered, the owner may file an application for the transfer of the registration and, where applicable, the license plates, accompanied by the certificate of registration of the first commercial car. The amount of any tax due or credit to be allowed for a transfer of registration under this division shall be computed in accordance with division (A)(4) of this section.
No commercial car to which a registration is transferred under this division shall be operated on a public road or highway in this state until after the transfer of registration is completed in accordance with this division.
(6) Upon application to the registrar or a deputy registrar, a person who owns or leases a motor vehicle may transfer special license plates assigned to that vehicle to any other vehicle that the person owns or leases or that is owned or leased by the person's spouse. As appropriate, the application also shall be accompanied by a Power of Attorney for the registration of a leased vehicle and a written statement releasing the special plates to the applicant. Upon a proper filing, the registrar or deputy registrar shall assign the special license plates to the motor vehicle owned or leased by the applicant and issue a new certificate of registration for that motor vehicle.
(7) If a corporation transfers the ownership of a motor vehicle to an affiliated corporation, the affiliated corporation may apply to the registrar for the transfer of the registration and any license plates. The registrar may require the applicant to submit documentation of the corporate relationship and shall determine whether the application for registration transfer is made in good faith and not for the purposes of circumventing the provisions of this chapter. Upon a proper filing, the registrar shall issue an amended certificate of registration in the name of the new owner.
(B) An application under division (A) of this section shall be accompanied by a service fee of two dollars and seventy-five cents commencing on July 1, 2001, three dollars and twenty-five cents commencing on January 1, 2003, and three dollars and fifty cents commencing on January 1, 2004, a transfer fee of one dollar, and the original certificate of registration, if applicable.
© Neither the registrar nor a deputy registrar shall transfer a registration under division (A) of this section if the registration is prohibited by division (D) of section 2935.27, division (A) of section 2937.221 [2937.22.1], division (A) of section 4503.13, division (D) of section 4503.234 [4503.23.4], division (B) of section 4510.22, or division (B)(1) of section 4521.10 of the Revised Code.
(D) Whoever violates division (A) of this section is guilty of a misdemeanor of the fourth degree.
(E) As used in division (A)(6) of this section, "special license plates" means either of the following:
(1) Any license plates for which the person to whom the license plates are issued must pay an additional fee in excess of the fees prescribed in section 4503.04 of the Revised Code, Chapter 4504. of the Revised Code, and the service fee prescribed in division (D) or (G) of section 4503.10 of the Revised Code;
(2) License plates issued under section 4503.44 of the Revised Code.
I put in bold the pertinent portions
Sees straight forward...if the old vehicles tags were not expired and you applied you good.
Read more: Ohio BMV says that you have 30 days to transfer plates from ... - JustAnswer http://www.justanswer.com/law/1c6tu-ohio-bmv-says-30-days-transfer-plates.html#ixzz21Xxi52b5