GOP presidential candidate Rick Santorum recently asked Google to remove the alternative definition of his name created by sex columnist Dan Savage from Google search results. It’s a defintion so unsavory we cannot even write about it, even though it’s the first definition to come up if you search “santorum.”

Rick Santorum. (Steve Pope/AP)

Santorum may take heart in knowing it’s not a piece of cake to get Google to take search results down.

The instances in which Google takes information offline are, as the company says, “very limited,” despite the legions of people who wish they could erase their Google history — including former Google CEO Eric Schmidt. When Schmidt once asked his company to remove search engine information about a political donation he made, Google politely declined.

Here’s when Google actually does remove or censor results:

1. When they get a court order.

In May, Google took down a blog covering the Amanda Knox murder trial called Perugia Shock after the head prosecutor of the case filed a lawsuit against the blog for defamation.

At the time, a Google spokesman told BlogPost: “After receiving an Italian court order, we have been forced to take down this blog. In an effort to protect free expression, we take care to narrow all court take down orders. Unfortunately, in this case, we would face criminal noncompliance charges if we refuse to comply.”

2. When it receives a complaint under the copyright act.

In October 2009, Google took file-sharing site Pirate Bay out of its search results in response to a complaint under the U.S. Digital Millennium Copyright Act. Google later put the site back in its search results.

In 2010, the search giant removed BT Junkie, a bittorrent search engine from its search results, once again citing a U.S. Digital Millennium Copyright Act take down request.

3. When someone tries to cheat.

When the German Web site of BMW was discovered in 2006 to be redirecting users from requested information to another page selling luxury cars, Google removed the Web site from its Internet search index altogether.

Google engineer Matt Cutts said that including hidden software like BMW did was “a violation of our webmaster quality guidelines.”

The lesson Santorum should learn from all this?

Hope that Savage either starts cheating search results or breaking the law. Alternately, we suggest Santorum look at this handy dandy search removal tool from the folks at Google.