The only way this happens is if large parts of the world are turned into police states, and forced at gunpoint to adhere to the family planning wishes of the eugenics movement. Or the world is turned into a total hellhole. Or somehow, the developed nations institute zero birth rates and draw their entire population from the rest of the world, and then indoctrinates the newcomers with the same ideology, which is just bizarre and totally at odds with the population control agenda.
Uh, what?
Developed nations generally have very low birth rates, at replacement or below (sometimes far below) - there's no 'instituting' anything, it's just a natural consequence of child survival rates approaching 100% and it costing a quarter of a million dollars to rear each offspring.
Third-world countries have very high birthrates with very high mortality until someone introduces modern-ish medical principles and enough food to avoid starvation, at which point the population explodes. Then, if the economy keeps up, eventually the country becomes 'developed', the population stabilizes, and they start importing third-worlders to do the dirty jobs.
Everyone gets all hung up on china, but it's very much the exception that proves the rule.
The whole 'ocean of humanity' phenomenon is mostly due to countries which have got stuck at the 'moderate poverty' point where their populations can manage to keep most of their kids alive but don't have the education and economic prospects to decide that they and their kids will be better off with a smaller family.
Compare these two maps:
http://en.wikipedia.org/wiki/File:Countriesbyfertilityrate.svg
http://en.wikipedia.org/wiki/File:WorldMapLiteracy2011.png
Get all countries to some moderate degree of development early (say, world-wide literacy rate at 95% by 1950) with decent economic growth (even 2% a year is probably enough) and it will mostly take care of itself. How you accomplish those herculean task is another matter, obviously. The easiest thing is probably to avoid half the planet getting stuck in various central planning dead-ends and smashed up by wars.
Take india as an example - nowadays the birth rate is down to something like 2.3 which is about replacement level. The sooner this level is reached, the less the population balloons before stabilising.
OTL economic growth was approx 1% a year for the 30 years after independence due to mismanagement of the economy. Make that 2% and the economy in 1977 would be a third larger than OTL. 3% makes it 80% larger.
Assume that does not impact the population growth for the first 30 years and you have 345MM at independence, 630MM in 1977 as OTL. If the extra wealth then halves the rate of population growth then the 2013 number becomes 925MM instead of the OTL 1,220MM - 295MM people (24% of OTL population) have vanished. That's not taking into account all the complexities about lengthening life expectancy, population structures and whatnot which obviously complicates matters.