I got this from the help file (sometimes it "helps", sometimes it doesn't) :
Types of Breaklines
Define standard, proximity, wall, and non-destructive breaklines for a TIN surface.
Standard. Defined by selecting 3D lines, grading feature lines, and 3D polylines.
Proximity. Defined by drawing or selecting a grading feature line or polyline object in the drawing within the extents of the surface boundary. The XYZ coordinates of proximity breakline vertices are determined from the surface TIN points that are in closest proximity to the corresponding vertices of the defining points or entity.
NoteTo specify breaklines from points, first convert the points into 3D or 3D polylines using the ’PN command. For more information, see Transparent Commands.
Wall. Defined using grading feature lines, 3D lines, 3D polylines, or by specifying points. A wall breakline is stored as a standard breakline, but defined differently: you provide an offset side for the entire breakline, and an elevation difference for each vertex, or for the entire breakline.
Non-destructive. Defined using grading feature lines and open or closed AutoCAD objects. A non-destructive breakline maintains the integrity of the original surface.
You can also import breaklines from ASCII FLT files into the surface definition.
The answer to your question about points for breaklines is found in the "note" above!
Hope this helps.
Nick R