#!/usr/bin/awk -f

/^\$$/ {
 print >file
 close(file)
 file = ""
 next
}
{
  if (file == "") {
    file=$0
  }
  print >file
}
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Then just run (assuming this is saved as split_big_file):

split_big_file big_file
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( Oh wait, ah, this isn't awkmonks? Sorry, wrong monastery... ) Well, errrm, just take the previously mentioned file, and run:

a2p split_big_file
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to get the perl version :-)

Updated. Fixed close statement (put parens around 'file' arg). Changed 'continue' to 'next' (although the awk worked-it didn't complain anyway, it confused a2p).