Points, also known as 'nodes' or 'joints', are automatically added at the I (start) and J (end) points of pipe, component, and frame elements. A tee is different in that it has 3 end points and an internal point at the tee centerpoint.

If a point or pipe support is drawn or inserted along the length of an existing pipe, frame, or component, those elements will be properly meshed for internal analysis, but the pipe or frame element will keep its original length. This functionality has the benefit of enabling users to move/slide point and support locations without having to manually divide the piping or frame elements.

If concentrated point loads, imposed displacements, or SIFs have been assigned, those assignments are automatically moved along with point/joint locations. 

To divide pipe elements in order to delete or make assignments (change pipe size, assign loads, etc.) for a selected area, users need to select piping along with points where you want to divide the section, then Edit menu>Edit pipes>Divide pipes. If there is no existing point at the location where the user wants to divide, then draw or insert one. The most commonly used option to divide/mesh pipe is to "Break at intersections with selected joints". 

Here we drew (or inserted) pipe with a guide. This modeling approach divides the piping as shown below left.