What party is responsible for ensuring that a public corporation's total number of outstanding common...

A corporation’s charter specifies the maximum number of authorized shares it may issue. The Registrar (provincial securities administrator) ensures compliance so that a public corporation does not issue more shares than authorized.

Trustees oversee debt obligations.

Portfolio managers manage investments.

Distributors sell securities but do not regulate share issuance.

Thus, the responsible party is the Registrar.