Are there diversion points for southern Pacific great circle route flights?
This particular flight was a Boeing 747 flying from YSSY (Sidney) to SCEL (Santiago).  Because a 747 has more than two engines, they don't have specific time limits on how far from land that they can fly like two engine airplanes do.

That being said, they do have to carry enough fuel to make it to a suitable airport in the event that the airplane depressurizes or it has an engine failure at any point along their route.1.  This doesn't mean that they have to make it all of the way to their destination in the event of a problem though.  They use en-route diversion airports and have predefined points on their flight plan which tell them where to divert to at any given point during the flight.

You will notice on this flight (see the images below) that their planned route is considerably further North than the shorter great circle route.  This is probably so that they can use NTAA (Tahiti) as a diversion airport if they have a problem.  The route is also optimized for the current winds at the cruising altitude, so it may be more fuel efficient to go out of the way in order to have more favorable winds.  

In this case, without seeing their actual dispatch paperwork we can't know for sure whether or not they could have even flown the great circle route with the amount of fuel that the airplane can hold, but we'll just assume that they are using NTAA as an ETOPS airport for the purposes of this discussion.  That being said, we will use the following airports as our ETOPS diversion airports:  NZCH, NTAA, and SCEL.  In this case, their diversion plan in the event of an emergency would probably be something like this:


From takeoff (YSSY) until a point a little less than half way to NZCH (New Zealand)2 they would divert back to their point of departure2
From a little less than half way to NZCH until a point around 46W52 they would divert to NZCH.
Between the points that would be around 46W52 and 47W25 they would divert to NTAA.
After 47W25 they would continue on to their destination (SCEL) because it would be faster than turning around and going back to any of the other airports.


Each of the points takes wind into consideration, and as they pass each one they will always know which airport that they can reach in the least amount of time.  The most important thing is that they always have enough fuel to make it somewhere safe in the event of an emergency.


Filed Route


Great Circle Route



1 They also have to carry enough fuel to fly to their alternate airport and additional contingency fuel.  One thing to keep in mind is that a jet burns considerably more fuel at low altitudes than they do at their optimum altitude, so they have to carry a lot of extra fuel to meet this (and other) requirement.

2 If they turned around at the exact halfway point, it would take them longer to return than to continue because of the East winds.



Regulations

For those of you interested in the actual fuel requirements for a flight like this, the US regulations are listed in 14 CFR 121.  I'll use these as an example (other countries will be very similar, but I know these.)

You will notice that almost every line of the regulations listed here will require extra fuel to be on board the airplane. (Look for the ✈ symbol next to each one that I have added.)  Fortunately, it isn't quite as bad as it looks though, because some of the fuel that is pumped into the airplane can be used for more than one purpose.  For instance, a portion of the fuel may be used to divert to an ETOPS airport and used to fly to your destination, because they will only be doing one or the other.  The pertinent regulations are summarized here:


  §121.645 - Fuel supply: Turbine-engine powered airplanes...
  
  ...
  
  (b) For any certificate holder conducting flag or supplemental
  operations outside the 48 contiguous United States and the District of
  Columbia, unless authorized by the Administrator in the operations
  specifications, no person may release for flight or takeoff a
  turbine-engine powered airplane (other than a turbo-propeller powered
  airplane) unless, considering wind and other weather conditions
  expected, it has enough fuel—
  
  ✈ (1) To fly to and land at the airport to which it is released;
  
  ✈ (2) After that, to fly for a period of 10 percent of the total time
  required to fly from the airport of departure to, and land at, the
  airport to which it was released;
  
  ✈ (3) After that, to fly to and land at the most distant alternate
  airport specified in the flight release, if an alternate is required;
  and
  
  ✈ (4) After that, to fly for 30 minutes at holding speed at 1,500 feet
  above the alternate airport (or the destination airport if no
  alternate is required) under standard temperature conditions.
  
  ...
  
  §121.646 - En-route fuel supply: flag and supplemental operations.
  
  (a) No person may dispatch or release for flight a turbine-engine
  powered airplane with more than two engines for a flight more than 90
  minutes (with all engines operating at cruise power) from an Adequate
  Airport unless the following fuel supply requirements are met:
  
  (1) The airplane has enough fuel to meet the requirements of
  §121.645(b);
  
  ✈ (2) The airplane has enough fuel to fly to the Adequate Airport—
  
  ✈ (i) Assuming a rapid decompression at the most critical point;
  
  ✈ (ii) Assuming a descent to a safe altitude in compliance with the
  oxygen supply requirements of §121.333; and
  
  ✈ (iii) Considering expected wind and other weather conditions.
  
  ✈ (3) The airplane has enough fuel to hold for 15 minutes at 1500 feet
  above field elevation and conduct a normal approach and landing.
  
  (b) No person may dispatch or release for flight an ETOPS flight
  unless, considering wind and other weather conditions expected, it has
  the fuel otherwise required by this part and enough fuel to satisfy
  each of the following requirements:
  
  ✈ (1) Fuel to fly to an ETOPS Alternate Airport.
  
  ✈ (i) Fuel to account for rapid decompression and engine failure. The
  airplane must carry the greater of the following amounts of fuel:
  
  ✈ (A) Fuel sufficient to fly to an ETOPS Alternate Airport assuming a
  rapid decompression at the most critical point followed by descent to
  a safe altitude in compliance with the oxygen supply requirements of
  §121.333 of this chapter;
  
  ✈ (B) Fuel sufficient to fly to an ETOPS Alternate Airport (at the
  one-engine-inoperative cruise speed) assuming a rapid decompression
  and a simultaneous engine failure at the most critical point followed
  by descent to a safe altitude in compliance with the oxygen
  requirements of §121.333 of this chapter; or
  
  ✈ (C) Fuel sufficient to fly to an ETOPS Alternate Airport (at the one
  engine inoperative cruise speed) assuming an engine failure at the
  most critical point followed by descent to the one engine inoperative
  cruise altitude.
  
  ✈ (ii) Fuel to account for errors in wind forecasting. In calculating
  the amount of fuel required by paragraph (b)(1)(i) of this section,
  the certificate holder must increase the actual forecast wind speed by
  5% (resulting in an increase in headwind or a decrease in tailwind) to
  account for any potential errors in wind forecasting. If a certificate
  holder is not using the actual forecast wind based on a wind model
  accepted by the FAA, the airplane must carry additional fuel equal to
  5% of the fuel required for paragraph (b)(1)(i) of this section, as
  reserve fuel to allow for errors in wind data.
  
  ✈ (iii) Fuel to account for icing. In calculating the amount of fuel
  required by paragraph (b)(1)(i) of this section (after completing the
  wind calculation in paragraph (b)(1)(ii) of this section), the
  certificate holder must ensure that the airplane carries the greater
  of the following amounts of fuel in anticipation of possible icing
  during the diversion:
  
  ✈ (A) Fuel that would be burned as a result of airframe icing during 10
  percent of the time icing is forecast (including the fuel used by
  engine and wing anti-ice during this period).
  
  ✈ (B) Fuel that would be used for engine anti-ice, and if appropriate
  wing anti-ice, for the entire time during which icing is forecast.
  
  ✈ (iv) Fuel to account for engine deterioration. In calculating the
  amount of fuel required by paragraph (b)(1)(i) of this section (after
  completing the wind calculation in paragraph (b)(1)(ii) of this
  section), the airplane also carries fuel equal to 5% of the fuel
  specified above, to account for deterioration in cruise fuel burn
  performance unless the certificate holder has a program to monitor
  airplane in-service deterioration to cruise fuel burn performance.
  
  ✈ (2) Fuel to account for holding, approach, and landing. In addition to
  the fuel required by paragraph (b)(1) of this section, the airplane
  must carry fuel sufficient to hold at 1500 feet above field elevation
  for 15 minutes upon reaching an ETOPS Alternate Airport and then
  conduct an instrument approach and land.
  
  ✈ (3) Fuel to account for APU use. If an APU is a required power source,
  the certificate holder must account for its fuel consumption during
  the appropriate phases of flight.
  
  §121.647 - Factors for computing fuel required.
  
  Each person computing fuel required for the purposes of this subpart
  shall consider the following:
  
  ✈ (a) Wind and other weather conditions forecast.
  
  ✈ (b) Anticipated traffic delays.
  
  ✈ (c) One instrument approach and possible missed approach at
  destination.
  
  ✈ (d) Any other conditions that may delay landing of the aircraft.
  
  For the purposes of this section, required fuel is in addition to
  unusable fuel.