What shape for the edges of a pot and what surface properties are best for a tea pot not to spill? Apart from the cross-section from the side, how does the radius of curvature as seen from above play a role? Ideally it should also stop drops coming down. And how does that depend on the properties of the liquid inside?
The phenomenon you are asking about is known as the "teapot effect". The mystery is why tea dribbles down a pot's spout despite relatively high Weber numbers being associated with the flow. Such high Weber numbers indicate inertia should dominate over surface tension. Recent research has indicated the physics of pouring tea is more complex and does involve surface tension and contact angle effects due to these influencing the flow geometry even at high Weber numbers.
So although particular spout geometries (sharp edges) do help, the elimination of the teapot effect lies in the use of superhydrophobic spouts. The authors of the 2009 paper demonstrate that this completely eliminates any tea dribbling down.
It is a study experimentally and by models of fluidity, as the title says, of the motion of coffee as one walks with a cup. It does not directly answer the question above, as it is not talking of drops after pouring the liquid.
It gives ways to control coffee spilling,
The best way to prevent coffee spilling might be to find an unusual cup. According to Krechetnikov, ideas from liquid sloshing engineering studies, which historically were done to stabilize fuel tanks inside missiles, indicate three possibilities for spill-free cup designs: "a flexible container to act as a sloshing absorber in suppressing liquid oscillations, a series of annular ring baffles arranged around the inner wall of the container to achieve sloshing suppression, or a different shape cup.
I still think that my aunt's suggestion at church tea parties to put the spoon in the teacup when taking it to the seated aunts is the best way not to spill it :).
Going back to the original question I will summarize my comments in "it is the edge" and that is why a lot of ingenuity has gone into designs of tea spouts available in the market. I have a cheap one liter water heater which has a plastic container. In the beginning it did not drip, but after two years the spout has deteriorated, not visibly, but obviously since it is now dripping. Either the heat or salt accumulation has changed the edge.
Edit: the ruminations of a chemical engineer turned potter on how to make drip free spouts