I've spent a day writing and rewriting my answer because while it's actually pretty simple, it can seem more convoluted than it is.

There's a few different categories of estates; The Monarch's personal landed titles and estates, the wide range of fiefs, and what we can call 'private property' that was owned by someone but had no noble titles attached.

The lands the monarch would have direct control over would be his own personal duchies or counties; The titled estates that were his right regardless of if he's the king. And control over whatever small landholdings they chose to buy privately.

For example Henry II Plantagenet was the Duke of Normandy and Count of Anjou prior to becoming King of England, and then with his marriage to Eleanor he was Duke of Aquitaine. Another is Frederick Barbarossa being the Duke of Swabia.

The Monarch also had direct control over what I'm going to call as "the bank" of various fiefs and estates. Not all titles were hereditary and many that were would still have the family line die out.

These often fall under what's called the Crown or Reich lands in the case of the HRE and are officially legally separate from the Monarch's personal lands but as monarch has the right to administer and distribute as he wishes.

The monarch also has the right to take away the lands and titles from one of his nobility if required but can be politically dangerous if the collective nobility feels that it's being done unlawfully. In the HRE this is an Imperial Ban and makes the banned an outlaw who lost his legal control over his properties and can be arrested or killed.

For example. Frederick Barbarossa had a rival in Henry the Lion who was both Duke of Saxony and of Bavaria. As Henry often challenged Barbarossa, the Emperor banned Henry in 1180 and invaded Saxony and seized Bavaria. Henry submitted to Frederick and then Frederick returned the title of Saxony to Henry. (Saxony was given to another Count named Bernhard with Henry in exile but henry later returned from exile and retook some of Saxony for a time, its a whole thing)

But the Emperor bestowed Bavaria on his loyal servant Otto Von Wittelsbach, whose descendants ruled Bavaria until 1918.

There was always an amount of lands & titles "in the bank." As not all titled estates were hereditary as I mentioned before but also many that were hereditary had a limit to who was eligible to inherit the lands. In this case it would be Father to son or brother to brother but not to like first cousin to first cousin.

Now that 'first cousin' could petition the monarch to be granted the lands but it was up to the monarch to agree. The monarch benefited from the "bank of lands" as they would collect the rents directly but had to appoint Castilians or managers to run the properties. It was often easier to grant the lands to the "first cousin."

The last category of lands are those "private properties." These are lands that hold no titles but may be valuable monetarily or resource wise. Vineyards, orchards, farm or woodlands. Lands that anyone could own, even free peasants, and were used to supplement income or hunt or retire in peace.

Now, the monarch can permanently add properties from "the bank" to his own private ownership but it was seen best politically to give his own lands to "the bank" in fair exchange rather than hoarding it all.

In a hereditary monarchy like England, the king's lands and the "Crown's land" were functionally the same but the difference was extremely important in the Holy Roman Empire, even though the imperial line did usually follow dynastic lines, it wasn't guaranteed.

Returning to my main example of Frederick Barbarossa. Frederick was the Duke of Swabia and as such an extremely powerful lord, his Uncle Conrad was the King of Germany.

Conrad had a young son but when Conrad died, the Princes of the Empire didn't want a minority monarchy and with young and strong Frederick there, he secured the election and was crowned King.

But Conrad's young son, also confusingly named Frederick,( it's a Hohenstaufen thing) was seen as being deprived of his rightful inheritance. To make up for the loss of the Crown, Barbarossa chose/had to give his little cousin the Duchy of Swabia, losing his direct powerbase.

Now Frederick as King and Emperor, he had access to the wealth of the "bank of lands" the Reich lands of Germany, he was also the King of Italy and the King of Burgundy so their "banks", his personal private properties, and of course the loyal feudal obligations of his princes.

After that, Frederick tried to cross the Alps and reorganize The Kingdom of Italy as his personal powerbase after losing Swabia but it was to mixed success and eventually failed. The only long term benefits to Barbarossa was that so many nobles, including his young cousin, died of disease that he was able to regain Swabia and replenish "the bank" and better secure Germany. Learning the hard lesson of many Emperors and Kings, Italy was a sink pit of gold and men.

I hope I was clear and please follow up with any questions if you have any.