I agree that math circles must be regional. I had never heard the term until reading it here on CC. Our school didn’t even offer the AMC until several years ago, and even then, not consistently. No one at his school practiced or prepped for AMC or AIME.
My son ended up on the ARML team, but as @sunnyschool said, by seeking it out on his own. It wasn’t until l his Sr year, so it had no bearing on college admissions. Driving him to the ARML practice session was quite eye-opening. I had no idea this existed and that some families had been participating for years. Thinking back on this, he may have sat for an exam Jr year also, in an attempt at qualifying for ARML. Details are hazy, but I recall that he had to travel 15 or 20 minutes to find a school where he could sit for the exam.