You get a polymer!
When you have ethylene glycol react with phtalic anhydride in a basic sollution such as NaOH(aq) you'll get a linear polymer.
When you have glycerol react with phtalic anhydride in the same way you'll get a crosslinked polymer.
The important difference between glycerol and ethylene glycol is the amount of OH groups, and as we all know, the OH groups usually the group that reacts - particularly in the creation of polymers.
So in this case your crosslinked polymer will be the glycerol as it has 3 OH groups. One in each end, allowing the molycule to connect with other molecules and create polymers, and one in the middle (connected to the 2nd Carbon Atom) allowing it to react with other polymers.
I hope that sort of answers your question