It didn't really happened the same in most of Romania than in post-imperial Britain : there imperial and local structures were ruined, and Germanic population came in small waves of familial settlers. In, say, Gaul or Spain, we have essentially mercenary/federate groups that lived on both banks of the limes since centuries or, at worst, decades, and that didn't as much settled in familial groups than directly intermixing with Roman or romanized populations in a quick process.
There's also a different pattern with regions as Illyricum that depended a lot on military presence for the organisation of the provinces, and when taken over eren't really the epithome of Roman civilisation and remained largely underpopulated, allowing waves of familial settlers to really kick in in the VIth century onwards, leaving a complex mosaic of cultural communities eventually dominated by Slavs.