I am familiar with all the debates around/about this topic.
Are both ‘around’ and ‘about’ equally good in the above context? Do they both mean the same thing?
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I would go with about — at least in more formal situations.
Although the Oxford English Dictionary shows a few example usages for around in the sense of concerning (the first at 1897), it seems to me (and to this writer) that this usage has only relatively recently gained traction.
Lastly, I would have you look at debate the verb and then make your decision:
We debated about this topic. There was a debate about this topic.
We debated around this topic. There was a debate around this topic.
For precision’s sake, I would use around only where surrounding makes sense:
I am familiar with all the issues surrounding this topic.
I am familiar with all the issues around this topic.