What is the ratio of actual flight time to simulator time on type for airline pilot training? I know that training flying time on large commercial aircraft is awfully expensive but I'm just curious how much training time a typical scheduled passenger airline pilot gets on the real craft these days? In particular I'm motivated by investigation reports that reveal that current simulators may have flaws and shortcomings in realistically simulating some parts of the flight envelope. 

I'm sure this varies  a lot by pilot, airline etc. so I'm not at all looking for an exact answer, just a approximate figure. 

e.g. Say, I'm flying on a A-320 or a B-787 commanded by a newly type-certified first-officer, what could be the bare minimum actual flight time (not simulator time) on an A-320 / B-787 that he could have had? 

PS. What is the type-rating process? Does that have no need for flight time? Can you get Type rated with 100% sim time on type?
Zero hours in type.

The first time a new FO flies the actual airplane could be their first revenue flight with a training captain in the left seat.  Technically, these flights are still considered training, specifically "initial operating experience" (IOE) and a few trips will be flown with training captains before the new FO is released to fly with regular line captains.  IOE is conducted on revenue flights though, so its entirely possible that the before your flight leaves the gate that the FO has exactly 0 hours in type.

The initial training (leading to either a full type or an SIC type) and the upgrade training (full type ride if you only had an SIC type) are 100% in FTD and level D FFS (full flight simulators) and the checkride is in the FFS.