The code below will spawn as many children as possible. Themselves won't fork further, and will become zombies once the parent process exits.
How many children processes will the parent process spawn ?
int main(int argc, char *arg[])
{
while(fork() > 0);
}
The number of child processes can be limited with setrlimit(2) using RLIMIT_NPROC. Notice that fork(2) can fail for several reasons. You could use bash builtin ulimit to set that limit.
You can use getrlimit (or parse /proc/self/limits, see proc(5)) to get that information.
System-wide, you might use /proc/sys/kernel/threads-max since:
This file specifies the system-wide limit on the number of threads (tasks) that can be created on the system.
There is also /proc/sys/kernel/pid_max
This file specifies the value at which PIDs wrap around (i.e., the value in this file is one greater than the maximum PID). PIDs greater than this value are not allocated; thus, the value in this file also acts as a system-wide limit on the total number of processes and threads. The default value for this file, 32768, results in the same range of PIDs as on earlier kernels. On 32-bit platforms, 32768 is the maximum value for pid_max. On 64-bit systems, pid_max can be set to any value up to 2^22 (PID_MAX_LIMIT, approximately 4 million).
However, there could be other limitations (notably swap space).
A task for the kernel is either a single-threaded process or some thread inside some process - e.g. created by low-level syscall clone(2) (or some kernel thread like kworker, ksoftirqd etc...).
BTW, the practical number of processes is much more limited by available resources. A typical Linux desktop has only a few hundreds of them (right now, my Debian/x86-64 desktop with 32Gb RAM & i5-4690S has 227 processes). So a process is a quite expensive resource (it needs RAM, it needs CPU...). If you have too many of them you'll experience thrashing. And in practice, you don't want to have too many runnable processes or schedulable tasks (probably only a few dozens of them at most, perhaps no more than a few per core).