Full papered is a term that simply means that the horse's dam, grand-dam, and  great grand-dam are all STER (top 10% of all mares) or MODEL (top 2% of all mares).  PREFERENT  means that the horse has many STER offspring, and it is an indication that they have excellent quality offspring.  If you are looking at a horse from Legacy Friesians that is NOT full papered, it just means it is "regular papered" and don't worry, it is still a REGISTERED FRIESIAN WITH PAPERS (all our horses are)!!!!   Full paper is analogous to coming from a family that is good looking, smart, and athletic, generation after generation.   In the USA, families like that are hard to find, right, maybe the closest family I can think of is the Kennedy's?  But then there is Ted Kennedy and he would never get STER.   Same for Friesians.  Full paper horses are very rare and more expensive.  Buying a Full paper horse for breeding is worth the extra money.  Buying a full paper gelding is not really necessary because they won't be breeding, but it certainly means that they have a good pedigree! 
 
 

How to interpret Friesian pedigree diagrams:

When they are STER, an S follows their name. 

When They are Model, an M follows their name. 

When they are STER plus PREFERENT  S+P follows their name

When they are MODEL plus PREFERENT  M+P follows their name.  Model+Preferent is the highest ranking you will find for Friesian mares.
 
 

EXAMPLE: the gelding below (Hearke B.) has the FULLEST paper that any horse can have!
Model+Pref -  Model+Pref - Model+Pref - Model+Pref!!!
 

ANOTHER EXAMPLE: the filly below (Tessa PJ) also has a full paper pedigree:
Ster - Ster - Ster

 
 
 In America, a FULL PAPERED filly or mare would be a very good idea if you plan to breed Friesians in the future.  We know from experience that there are a lot of customers who only want to buy full papered colts or fillies.  So if you want to breed foals that are full papered for the discerning customer, you need to purchase a full paper filly.  Some breeders like to have a wide selection of broodmares,  where some of their mares are full papered star mares, and other are normal papered studbook mares, so they can offer a broad spectrum of foals with a range in prices.  The full papered foals will be more expensive, of course.

However, if you want to buy a gelding for dressage, it is actually not critical to buy a full papered horse.  This is because the gelding is not going to be bred.  And also the criteria for the STER and MODEL are based on the opinion of traditional Dutch judges who tend to like to see a lot of knee action, not based on dressage suitability.