We lawyers can add hundreds of words, and thousands of dollars, but this should be sufficient for your needs if you can't spend lots and lots of money on it.
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Generally, this should be okay for the logo only. You may want to use "rights" and not "right." It is reasonable to have more than a single right when relating to intellectual property.
This is not a legal advice as I do not have an attorney-client privilege with you. You should retain a lawyer before acting on any generally available advice.
Typically, when I'm representing the individual or company HIRING the contractor (as opposed to the contractor himself/herself), I try to follow a "multi-layered defense" approach. For example, in the context of works of authorship protectable under copyright law, there will ideally be ~5 distinct layers (number of layers and specific language for OTHER types of protectable intellectual property, e.g. trade secrets, patentable or non-patentable inventions, etc., will differ somewhat):
(1) All Work Products hereunder will be deemed to be "works made for hire" with exclusive right, title and interest thereto, together with all intellectual property rights therein, vesting in Company from the moment of their creation.
(2) To the extent that any Work Products hereunder are determined NOT to constitute "works made for hire," Contractor agrees to assign and hereby does assign to Company all right, title and interest thereto, together with all intellectual property rights therein, immediately following their creation.
(3) Should both Sections (1) and (2) fail of their essential purpose for any reason with respect to any particular Work Product(s), Contractor agrees to grant and hereby does grant to Company a worldwide, perpetual, irrevocable, fully paid up right and license to use, create derivative works and sublicense (through one or more layers) said Work Product(s), together with all intellectual property rights therein, for any legal purpose.
(4) Contractor will execute such documents and take such other actions as Company may reasonably request from time to time, at Company's expense, in order to transfer, evidence and perfect the rights to which Company is entitled pursuant to Sections (1), (2) and/or (3) above.
(5) Should Contractor be unwilling or unable to follow through on its obligations as described in Section (4), Contractor hereby grants Company a limited power of attorney, acting in Contractor's stead, to execute such documents and take such other actions as Company may deem necessary or appropriate from time to time, in order to transfer, evidence and perfect the rights to which Company is entitled pursuant to Sections (1), (2) and/or (3) above. This power of attorney is coupled with an interest and irrevocable.
Note that savvy contractors (or their attorneys): (i) will rightly want to reserve ownership of any reusable or generally useful Tools/Background IP which they used in creating Work Product, in which case I typically negotiate to at least make this stuff subject to a broad license under Section (3); and (ii) may bridle at granting an outright power of attorney as requested under Section (5).
THIS POST DOES NOT CONSTITUTE LEGAL ADVICE, DOES NOT IMPLY ANY ATTORNEY-CLIENT RELATIONSHIP, AND IS PROVIDED FOR GENERAL INFORMATIONAL PURPOSES ONLY.
In cases like this, I generally include a provision stating that the work performed under the contract is a work made for hire, and a provision stating that the contractor assigns all right, title, and interest in the work to the hiring party. I also clarify that this includes all trademark, patent, copyright, and other rights (etc., etc.).
I am an attorney, but I am not YOUR attorney. By providing free, generalized information, I am not entering into an attorney/client relationship with you, nor am I providing legal advice applicable to your particular needs.