Republic Vassals, how many for an Empire?

I always try to make them without getting tyranny, so just after a holy war. I also pick the richest province in an area. They are a GREAT way to make money, but beware of raiders.

I would recommend one per two coastal duchies. Maybe slightly less, depending on size of duchies. I try to give an honorary title to each Doge. So the Doge of Venice would always get the Master of the Hunt, and when he died, I would immediately give it to his successor. Keeps 'em happy.

I usually have three - Pomerania, Karvuna and Venice.

Don't make them too close to each other, or they will fight over trade areas instead of making money

In my Norse game I have the Republic of Holstein (making Denmark and Pomerania prosper), Finland (for Finland, Sweden, and Lithuania), Flanders (for Frisia, France, and England), and I just formed the Republic of Bordeaux (to cover the rest of France and northern Iberia). I find Republics are the most successful when separated by a minimum of three sea zones, giving each enough room to expand. Farther apart is better, but areas with dense coastlines (such as England or Scandinavia) can generally support them closer. Keeping crown authority above medium is an absolute must to prevent costly embargo/trade wars between rival republics. It's also advisable to not let them grow beyond a single duchy and a handful of counties (titular duchies are great for this) as Republics in large stable empires tend to be the most powerful vassals, often being at the centre of annoying rebellions. If you can get and maintain your dynasty as one of the Patrician families, that goes a long way to controlling them.

I believe that each Rep should have 25 sea connected provinces for their own. So put one each 25th costal province.

Mid game its too dense, so you will most probably need to distroy every second one. So each have 50 costal provinces...