Varied root supplies affect the long life and looks of implanted cactus:

http://remingtonoepe619.yousher.com/the-pros-and-cons-of-grafted-cactus-vs-own-origin-cactus

Myrtillocactus geometrizans and Harrisia jusbertii are reputable choices, for different environments, making sure lasting grafts. Acanthocerous sp. is a fast-growing origin stock, although it presents challenges