There's no simple answer to your question that could even be categorized as a generalization. Some school programs take great care in selecting all levels of coaches if they want a big-time successful program and feel that it is an integral part of their school's persona. In those cases, the varsity coaching staff has most of the input into the freshman, sophomore and JV staffs.
In other school situations, there is much less emphasis on athletics and the AD might just take whoever he can get.
I have found the relative size of schools are not as much a factor in these decisions as you might at first think.
FYI - there is a program here that is so sophisticated that the varsity coach influences the selection of the middle school and elementary school classic coaches because he knows that eventually, those players will feed into his system. They also run his plays and use his terminology.
Everyone in the Portland area knows who this is, and - it works.
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Yom HaShoah
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