My (KWPN) boy was 16.2h as a 3YO and as a 4YO he's 17.1 and might go more. Hopefully not too much more! He's definitely filling out now though, I had to go up a size (wider) in his Bossy Bib this year, even though he's technically still in the same height range as last winter.
I have purchased 5 broodmares as 3 year olds (actually, 3 1/2 by the time they arrived in Canada). They grew 1/2" to 3/4 " in the following 2 or more years, putting them all in the 16.1 to 16.3 range.
A few (3 or 4) homebreds also grew less than 3/4" after 3 years of age. One gelding added fully 2" after 3 years of age.
Depends on the individual and their pedigree/genetics but as a general rule - anywhere from 0-5".
One of the 2007's was right at 17 hands in April. He's pushing 18 now. As a 3 year old, he was about 16.2. Another one of that group was 15.2 and is past 16.1 now. He was 15 hands as a 3 year old. Another was 15.3 and is now pushing 16.3 (behind) and 16.2 up front - he looks like a yearling from the withers forward with an adult horse back end. As a 3 year old, he was a tad more coordinated looking and about 15.3.
Of the current 3 year olds -
1 is 17 hands. I expect at least 2" more. (gelding)
1 is 16.2. I expect another inch, maybe 2. (mare)
1 is 15.3 1/2. He'll get at least 1-2" taller. (gelding)
1 is 16.1 and should 'only' add another inch. (mare)
We had a yearling that was 16.3 back in the early 80's (1/2 TB 1/2 Westphalian) - he finished at 16.3 1/2, so they can fool you sometimes. (or scare the hooey out of you depending on your frame of mind) Sire was 16.2, dam was 16.3.
As a rule, I look to the grandparents and average height from those 4, rather than the parents.
ETA: Ours break down (usually) to roughly 50% warmblood (Hanoverian, Westphalian, Oldenburg) and 50% TB by pedigree.