A mature colony of nitrifying bacteria can double in 24 hours. Mature means that is has been running for at least a few months, a strong well established colony.
Konowing this, for ease of math, lets say you have a 10 gallon tank with 10 small fish, all the same fish, same size. 1/2 the media will handle the bio load of 5 fish, 1/10 the bio load of one fish. So, when you take 1/3 to 1/2 of your mature bio media, and set it up running on a new tank, it will sustain that 1/3 to 1/2 of a new bio load. Knowing that a mature colony of nitrifying bacteria can double in 24 hours, your existing tank is reasonably safe, as is the new tank, as long as you stock the new tank properly.
There are a couple of precautions you can take, testing daily for the first week is an obvious one. Do not feed the fish in the mature tank for 24 hours before taking the mature media, and feed lightly for the next week. Less food means less waste produced, giving the nitrifying bacteria a chance to catch up if needed. The same applies to the newly set up tank.
The last tank I did any sort of cycle on was a 65 gallon in early '04. I had a 10 gallon, 20, 29, 55, and the cycling 65. The 20 was a clone, the 29 was fishless, as was the 65. Everything since then has been cloned, they're listed in my profile.