For one-off investments (e.g. buying a bond), a certificate will be sent for each investment.
If you make regular payments into one investment (e.g. a KiwiSaver scheme), the managers are generally required to send a six month statement showing investments made in that period. However, you can ask for an updated statement at any time.
We recommend you file your confirmation documentation in safe place, to remain organised with the paperwork for your chosen investment.