Removing wall paper border

It depends on how well the glue is adhered to the wall.  If you are luck you might be able to pull it off with out much effort.  Using a 6 inch spackle blade can help to get under the paper.  Just try not to dig into the sheet rock too much or you will need to spend some extra time coating the area with some spackle to fill in any imperfections.  There is also release agent that can be sprayed onto the wall paper to loosen the glue. Just go to your hard ware store and ask the paint guy for the stuff.  

HTH

+1 to the no scoring wheels. Defninitely peel the outer vinyl layer to allow moisture to get to the glue... then, it's just a matter of how you get the moisture to it.

The $30 wallpaper steamers at Home Depot work great.  I bought one and once it heated up (it takes a little while), I was able to completely remove the border from a room within 15 minutes without even having to scrape.

Scoring wheels suck don't use them.  Buy a steamer used for wall paper removal.  Like this one

http://www.homedepot.com/p/t/100532752?productId=100532752&storeId=10051&langId=-1&catalogId=10053&ci_sku=100532752&ci_kw={keyword}&kwd={keyword}&cm_mmc=shopping-_-googleads-_-pla-_-100532752&ci_gpa=pla#.UV7hFVIv3Oo

IF you have any more projects it will pay for itself as compared to renting a steamer. 

Border is a tough animal as compared to typical wall paper.  Use a putty knife but be careful and wait until it's jungle humid in the room.  It helps.  Good luck

Yup, that's the one I have (sorry, $50, not $30).  Storing it isn't that big of a deal, though pitt.... it gets lent out to family members rather often, so I let it stay stored in their basements

okay... so I'm a rebel w/ the scoring wheel.
Here are my steps (I've done this more than a few times   )

1)  Scoring wheel... don't grind it into the wall, just enough to make some holes in the paper. (this will help for the hot water and spray to get to the glue under the paper.  If you accidentally score the wall, it's fine, that's easily fixable.  You'll have to plan on painting anyhow b/c the paint will be different under the paper).

2)  HOT WET SPONGE... as HOT as you can stand it. (oops almost forgot... Rub the HOT water on the paper).

3)  There's this spray you can buy at the hardware store to help disintegrate the glue.  Spray on and use a non-absorbing rag to rub it into the paper.

4)  Let sit a few minutes.  If there's a lot to take down, you may be ready to pull the first part by the time you work around the room.

5)  Take putty knife and a dobie (you know the dish sponge w/ the hard netting around it) and get to work.  Keep a trash can/bag nearby.

Man, I know about wallpaper...  I still have nightmares.  I tried EVERYTHING.  Scoring, chemical, steaming, on and on...

When it came down to it, the simplest basically worked the best.  I bought a cheap bug sprayer from Lowes or Home Depot and just loaded it up with HOT water.  As hot as it gets from the tap.  Pump it up as directed and spray down the wall.  Not drench, but light mist/spray.  Let it rest some.  Then with a puddy knife or fingers, just pull it down.

If you have a large room, you figure out how to spray ahead far enough that once you get done taking down the section you are on, the next one is ready to do.  Just spray ahead of your work.

Sometimes you get lucky and the glue dissolves easily and you can take entire panels/sections down.  Other times?  The nightmare times?  When you can only get pieces the size of a playing card off at a time if you are lucky.

Having smooth walls is better than textured as well.  The knife can get under it.

Good luck.  I'm glad you only have a border to worry about, not entire rooms.

ETA:  I'm not against the scorer and chemicals and such.  The do help a LITTLE.  But after you pay for them, mix them, take the steps to score the paper (and/or leave holes in the wall).  I could be ahead of you just using warm water.  They only seem to be fractionally better with more cost and time to use them in the long run.  OH, and I almost smashed the steamer.  It was not better than hot water and it worked at a snails pace.

I wish I could write a book about paper removal to offset the tons of money I spent trying to figure out a good way to do it.

I've used the home depot steam cleaner. I suppose the attachment to my rug steam cleaner would have worked as well, but I liked the large surface area of the tool. I have lent it out to friends, and storing it is not a major issue (but then again, I like to have gear. It sits in the garage when not being lent out with other home improvement gear....)

If the wallpaper or border has a coating, the scoring tool works well. Like someone else said, don't grind it into the wall, just score the top of the wallpaper. Then let the steam get under the surface and do it's job. I found I still needed in some spots to scrape with a putty knife, but it vastly simplified the job.

I tried that trick.  I didn't see an appreciable difference, but if you got it laying around the house anyway and it's only pennies to add it.  I say go for it!