So there's a distinction between a dukedom and a duchy. A dukedom is just the entitlement to the rank duke, and is entirely separate from a duchy, which are the lands which are ruled by a duke. While they are generally considered to be the same, and in medieval Europe they were often essentially the same, one is not necessarily attached to the other. Generally the development of dukedoms, or their equivalent for any rank, being granted as opposed to duchies is something that has occurred as kingdoms have been more centralised and moved away from the feudal system.

I can only answer for England, but the move away from awarding counties to people being granted earldoms really occurred across the 14th to 16th centuries and depended on a lot of factors such as the authority of the monarch making the grant, the location and the person being given the title. For example you have the Earldom of Suffolk being granted to Michael de la Pole in 1385 without any of the lands of Suffolk, but then 200 years later Thomas Howard was granted the Earldom of Suffolk along with land in the area (although not the entire county) and the positions of Lord Lieutenant of Suffolk two years later.

All of this was held at the pleasure of the King though, so, like all land in England and since , the absolute owner was the Crown, not a Duke or Earl. I'm not entirely sure what you mean by 'when did these lands become property of the government instead of persons' - it all ultimately belonged to the crown (except arguably in palatinate counties, but I don't know enough about them to say for sure either way).