Printing, as a technology, draws from several branches of science, but it's not typically classified under a single branch. Here's a breakdown:

* Physics: Understanding the mechanics of ink transfer, the properties of paper, and the interaction of light with surfaces (for digital printing).

* Chemistry: The composition and properties of inks, toners, and other materials used in printing.

* Materials Science: Developing new materials for ink, paper, and printing substrates.

* Engineering: Designing and building printing equipment, including 3D printers.

* Computer Science: For digital printing, algorithms, image processing, and software development play a significant role.

Therefore, while not a single branch of science, printing is heavily reliant on the principles and advancements in these various scientific fields.