Most centers are able to see at least 50-80nm into adjacent airspace. At the Enroute level, assuming aircraft are clear of conflict, I'm starting the handoff process anywhere between 4-6 minutes flying time from the border (figure jets in cruise do anywhere from 6-10 miles a minute), so that's a range of about 25-60 miles from the border. I'll do my best to have the guy on the receiving sector's frequency no later than 1 minute from the border, preferably 2.
Holding onto a handoff until the last possible minute is just asking for airspace busts, which I don't think many people on here realize is a separation error the same as getting two planes within conflict proximity :p.