Police of Reddit; how much is an operation hampered when a criminal/ crime crosses different jurisdictions?

I live in the UK and near the border of Avon and Somerset Constabulary and neighbouring Devon and Cornwall Constabulary and must cross between the two 20 times a week. So, how does this effect policing? Surely these lines are not set in stone, i.e. during a car chase. In addition, if a crime happens in one place, but the criminal is in another, how does the investigation work? Also, in the event of a major police operation, i.e. the Raoul Moat manhunt where it all took place in one area, what if, when hundreds of officers from one force are employed pursuing him, he had just hopped into a neighbouring jurisdiction. Would hundreds of that forces men than need to be mobilised etc instead?