Assuming one acquires an old URL or an URL from competition

To clarify, do you mean a domain?

yes, a domain URL.

Why quarantine it at all? Can't you look at the backlinks and tell if there is likely to be or not to be a problem with them? The content will likely be all new content that you've written, so that's already within your control.

ZydoSEO I was thinking about backlink profiles.

To answer the original question, "how long does it take to sanitize a domain" (and I've changed the word "url" in the title to "domain", so future searches can find the question)... I'm guessing that it depends on how unsanitary it was. ;)

This would involve previous uses, how bad the backlinks were, and what steps you've taken to clean them up if they were bad. I don't think you can just let the domain sit and assume any penalties will expire.

There have been two threads here in the past year referencing some Google advice that might be helpful... from John Mueller and from Matt Cutts... and they go into some of the different situations you might encounter....

Is buying a previously owned domain name still dangerous?
Nov 2012
http://www.webmasterworld.com/google/4515322.htm [webmasterworld.com]

My emphasis added below...

...I get the sense from John Mueller's comments that change of ownership and change of content have been big factors which Google has paid attention to for a while, but that some backlink histories had been so messy that bad algorithmic effects lingered on, even after reconsideration requests.

What John Mueller said in the third video suggests to me that Google really does want to facilitate development of old domains that are bought as the basis to build new and improved sites...

And, more recently...

Can deleted (expired) domains be tainted forever in Google?
April 2013
http://www.webmasterworld.com/google/4567497.htm [webmasterworld.com]

Matt Cutts discussed this topic recently in a Google Webmaster Help video posted on YouTube....

Can I buy a domain that used to have spam on it and still rank?
Matt Cutts - trt 3:32
Apr 10, 2013
http://www.youtube.com/watch?v=lGUw9oS5csI [youtube.com]

In answer to your question as you formulated it...

Would a domain name have any penalty or ban removed after it has expired?

...I think Matt's answer would be that the penalty is not removed just because of expiration. It would instead depend on the type of penalty. It would most likely also require clean-up, and some penalties are not easy to remove....

...If the domain had been owned by a churn and burn spammer who used every conceivable trick to milk the domain for rankings, and then tries to make some extra money by selling it, a buyer might be left holding the bag.

Essentially, buying a penalized domain would put you in a hole, requiring that you build your way out, but the exact answer depends on the particular history of the domain and the type of penalties it has.