Printing and enlarge are 2 different things, print is according the resolution of the camera and enlarge depends on a post process of enlargement that each Print laboratory does using different software and consequently a different algorithm.
So people can print depending on the camera resolution, the more resolution the bigger you can print, BUT! Resolution is not the same in cameras with small sensors than big sensors, 2 cameras can be 10 megapixels but sensor size will affect the quality considering we are printing the same size with both, also there are phones with 10 megapixels photos but the sensor size in 1/10 over the biggest sensor.
Check this link for the last point explanation
The paper quality affects the quality of the print, there is a wide variety of papers and not all suit good for certain pictures, so photographer experience here is the most important, hope you understand that is not going to Costco, CVS, Sams Club and those generic photography print labs.
Check out the art of choosing the right paper link
When getting the laboratory The technical proficiency of the operator is very important too, places like Costco, CVS, Sams Club they just train the employees for general jobs and /or automatic, Professional laboratories usually has people than like to do photography and print their photos, they have a wide experience with papers and all related steps to get the best.
Also a good print depends on the photographer artistic decision, settings used, camera and lens limitations, uncontrolled circumstances that affects artistic decision, check out this link to understand more about getting a single image.
