Tomato pasta sauce splits. Why?
If by "fresh tomato paste" you mean you're starting with raw tomatoes, that's probably your issue. Most tomatoes you grow in your garden or buy from the store are salad tomatoes - they're not meant for cooking, and will result in a watery sauce like you describe.

You want a "sauce" tomato. Roma tomatoes or almost any plum-shaped tomato work well. There are others, but they're harder to find.