After you pay a judgement...

what papers/forms are filed by the court? And is the attorney for the collector supposed to send me a copy? Also, how soon after payment are these documents supposed to be filed with the court?

The satisfaction of judgment is usually what the form is called. WHEN and WHO arranges for recordation varies by STATE law. I've read that some areas require the judgment creditor to record the satisfaction, in other states the debtor is to arrange it. I.e. provide the completed form for sig and arrange for recording (i.e. pay the fee.)

And of course you need to check with YOUR court (the court that issued the judgment) about their requirements, that would be my first call.

"Professional" judgment creditors often offer to arrange for the recording of the satisfaction as part of the settlement.