A controlling process is a Wolfram kernel or front end that handles input, output and scheduling for the computing processes. You can evaluate $MaxLicenseProcesses to check the maximum number of controlling processes available for your license. A computing process (also known as a “subkernel”) is a Wolfram kernel that executes computations while accepting input from and returning output to a controlling process kernel only. When parallel functionality is invoked, a number of such subkernels is launched with each controlling process.

Each standalone Mathematica session consumes one controlling process and can launch as many subkernels as are available, determined by the number of cores available on your machine and the number your license permits. The number of cores available on your machine can be checked by evaluating $ProcessorCount. Running two sessions simultaneously therefore consumes all available processes of a standard “2,2,8,8” single-user license. Starting a third session leads to a request for an additional activation key or a kernel license failure message.

Using MathLM, the controlling process is the number of network users that can use Mathematica simultaneously, also known as available client seats. The MathLM computing process is the total number of subkernels the clients can use.