These are the factors that matter for conversion (from the descr_campaign_db):
Code:
<founding_conversion_default_rate float="0.0002"/>
<neighbour_normalise_weight float="0.00015"/>
<governor_conversion_rate_offset float="0.0004"/>
<governor_conversion_rate_modifier float="0.0004"/>
<owner_conversion_default_rate float="0.0002"/>
Founding faction, owning faction, neighbouring cultures, governor.
Colonies and the like have "fast conversion" which will override those, but when it hits the cap, those other things re-assert themselves. I don't think population size has anything to do with it at all.