If you create a custom cartoon, do I automatically own “all rights” to use the work any way I want?

A custom illustration doesn’t mean the artwork is owned by you after it’s created. This should be negotiated in advance and it’s advisable to indicate this upon negotiating a fee to produce the artwork first. For instance, let’s assume I create a cartoon or humorous illustration for a direct-mail piece and we’ve already negotiated a fee. It would not be advisable to then take this same artwork and use it online, since we didn’t negotiate any additional usage after that.
A dual usage would be applied to that cartoon…meaning the greater the usage applied to a cartoon, the greater the licensing fee.
Therefore it is always best to provide as much information in advance of have either a cartoon created for a certain usage or how an existing single panel gag cartoon will be used. The rule of thumb is to always provide as much information up front, when requesting a cartoon. Negotiating fees for cartoons is easy to grasp, once the process begins.