I took a closer look at Raleigh and the Inland Empire which topped the rankings of my most recent urban core comparison.
http://swontariourbanist.blogspot.ca...an-growth.html
In the case of the Inland Empire, most of the urban core population growth turns out to have been a result of increasing household sizes. I'm pretty sure the rate of household growth was still above average, but definitely wouldn't rank it at #2 and probably not in the top 10.
As for Raleigh, the fact that the boundaries are largely based on mode share and density relative to the MSA average means that it would probably be more accurate to describe the area as "the most urban part of Raleigh-Cary MSA"... which is not saying a whole lot.
About a third of the growth was on the southern fringe of Raleigh. The S/E side of Raleigh is the "unfavoured quarter", which means it has lower incomes and hasn't experienced as much growth. As a result, the suburban-rural fringe is pretty close to downtown, and the combination of proximity to downtown and below average incomes means the census tracts there have sufficiently low auto mode share to qualify as part of the "urban core".
After that, I looked at the top 15 growing census block groups within "the most urban part of Raleigh-Cary", a good chunk of the growth in these was suburban style townhouses and apartments and infill SFH subdivisions, ex:
You did have a few infill projects that were more urban though, and relatively little urban decay.
Infill near downtown Raleigh:
Those 15 block groups (+the southern fringe) contained most of the overall growth in the "most urban part of Raleigh-Cary". The less urban parts, which are almost all truly suburban and auto-oriented, took in 95% of the region's growth.