Q: RUNNING MACBOOK WITHOUT BATTERY

Yes.... But it will only run at half the processor speed.

There’s one problem with running your MacBook with the battery removed. MacBooks and MacBook Pros automatically reduce the processor speed by about half when the battery is removed.

http://support.apple.com/kb/HT2332
http://www.tomshardware.com/news/apple-macbook-pro-battery-benchmarks,6643.html

I've bought used MacBooks off of eBay for my family, seven of them so far over the last 6 years. I've bought 8 batteries off of eBay sellers, just going with the cheapest. Only had one with a problem, it gave out after 6 cycles. That one was replaced under the warranty by the seller. The only other batteries that have been a problem were Apple branded batteries that started bulging. I've had two of those happen.

Apple doesn’t make any batteries. They buy them from the same manufacturers that the third party sellers are buying from. The only difference is that Apple has their logo imprinted on the battery.

I had too the same issue but a diff. Batt. was showing "Service Battery" and I was afraid thus I removed and using with the Adaptor only.

What I dnt understand is --- "Yes.... But it will only run at half the processor speed."  Could you pls. a little bit elaborate this one?

Thankx.