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“Two and a Half Men” is a whole other kettle of fish.

The hijinks and misbehavior of its former star brought the glare of unsought publicity to the show and led to production shutdowns while Sheen got rehab for substance abuse. But however high-maintenance he might have been, Sheen, with his portrayal of freewheeling, womanizing Charlie Harper, was the keystone of a series that attracted a weekly audience of nearly 15 million viewers this season.

There’s always the chance that Sheen and the producers could kiss and make up and he could come back. Stranger things have happened (although, in this case, it’s hard to think of one).

But what newcomer can measure up to Sheen’s legacy? Who can comfortably connect with the show’s time-tested premise (the ups and downs of bachelor life) and with the show’s remaining cast (particularly the high-strung divorced father, Alan, played by Jon Cryer)?

That guessing game has been in full swing for weeks, with rumored candidates including John Stamos, James Spader and Jay Mohr (representatives for whom say no deal is pending), as well as David Arquette (whose spokeswoman declined to comment).

Or what about James Franco, who seems to be up for anything (though, with any luck, not another dreary year hosting the Oscars)?

Or what about Will Arnett, even though he’s also been mentioned as a good fit for “The Office,” and, by the way, has a pilot deal for his own new series?

But all of these names assume Charlie Harper will be replaced by a similar character. What if the producers choose to go in a fresh, new direction?

For instance, the name of Jenny McCarthy has come up. Who knows how she would be written into the show (she’s guest-starred before as a sexy con artist). But who cares? With her sharing the bachelor pad with Alan and his teenage son, she could turn the show into a “Two and a Half’s Company.”

Or, for a real departure, how about Larry King (a seasoned pro who’s surely available right now) as an oft-divorced septuagenarian ladies’ man?

Or what about the most obvious choice of all, Betty White? Just go ahead and let her run with it. She’s funny, everybody loves her, and she’s already doing nearly everything else.

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EDITOR’S NOTE _ Frazier Moore is a national television columnist for The Associated Press. He can be reached at fmoore(at)ap.org