This is just an addendum to Steve's excellent answer, in case anyone sees this and wonders if Steve's answer is applicable to all TLDs mentioned in the revised question (COM, NET and ORG).
There are two types of TLDs - global TLDs (gTLDs) and country code TLDs (ccTLDs like .US for the USA or .CN for China). ICANN rules govern gTLDs only.
COM, NET, and ORG are all global TLDs, which means they are all governed by ICANN. Steve's answer is therefore applicable to all three of them.
While ccTLDs are not governed by ICANN, they usually have a lot of things in common with their gTLD cousins. However, they are free to play by their own rules in any way they'd like and sometimes have some bizarre requirements and practices.
Source: myself. :) I have worked for almost 13 years on the core engineering team for a large, prominent registrar.