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It's a trick question, right?  Only one of them would rank and the others would be at the bottom of the results because they were duplicates.  The one that would rank would probably be the one with the best links to it / highest authority If you're asking if they were all exact copies of each other with the same back links, which URL might rank higher than the others simply by virtue of it domain name, it would be a crap shoot but Moosa may be right.

Re-branding is great and 301ing from existing domain to the new one is also a good idea for this but always remember whenever you do a 301 from one domain to another domain there is always a small loss of link juice which might cause a fluctuation for few or many of your ranking position in Google. In my opinion the idea is not bad but tries to plan a strategy that aloe you to gain some quick and high quality link in that case so that it can minimize the ranking loss due to 301redirection. **do not go for subdomain **As far as not using a keyword in the new domain..I would always recommend you to do some competitor analysis for this and do not remove the keyword from the domain if most of the competitors are sung it as I still have an observation that Google give less (but still a value) to domain that contain keyword in it! Hope this helps!