With Split Meshes into Connected Components, an individual mesh is created for each connected component of the loaded surface triangulation.

For example, a surface mesh loaded from a single .stl file as shown below for two spheres, with a single mesh handle for all the objects.

Open the settings dialog for Reassign Mesh Material ID and observe that only one mesh is shown.

Now go back to Split Meshes into Connected Components. Since the command detects the connected components automatically and separates them into individual meshes, no settings are necessary. Just click Edit to run the command.

When opening the dialog of Reassign Mesh Material ID again, two mesh handles now appear for the two spheres.

Now, separately, the two meshes can be saved (Save Mesh), deleted (Delete Mesh), or assigned to different Material IDs (Reassign Mesh Material ID).