A blanket statement is not possible here due to the tolerances in the width specifications of tire manufacturers.
For example, Schwalbe tires fit up to 2.4, VEE up to 2.35, and Maxxis up to 2.5WT. For the kids' bikes Frechdax, Dreckspatz, Barney, and Bam Bam, it is advisable to use the factory-installed tire widths as a guideline.