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I definitely wouldn't want that design exactly, but am moderately competent at Illustrator, etc. But equally at a rate of one tatoo every 25 years I don't really mind spending a bit extra to get an expert to come up with something.
ad441-
If you want your art on yourself then make a design and ask someone to do it. I don't think it matters about illustrator. That logo you sent is fine to give to a tattooer.
But you'll get something much more interesting and special if you choose an artist who is motivated to use your design as something to work off. Obviously it's totally subjective and you might find your design more interesting and special than what a tattoo artist would make.If you just want that logo then many people will be able to do that well for you.
sorethroat
I would say you would probably end up with something better if you let them use your idea as a starting point. But if you really want that design then probably best just to stick with it.