Two. Icinga2 and nsca-ng. You can bring it down to one if you use Icinga2 as the test runner on the individual machines.

If you need to shard, no other binaries are involved, just a couple of changed configuration files and some SSL certs. Passive reports can go to any node; a simple load balancer will work fine without any form of hashing or federation required.

> There is nothing inherent in a polling model that limits its ability to scale

Aside from the additional processing requirements, such as SSH, NRPE, subprocesses, etc, you are also limited in that a polling process must be told in advance of new systems or services, whereas it's fairly easy to just have a new service or system start reporting and be immediately monitored.