Will the supplier arrange the connection of the system and correspondence with the electricity provider or is this my responsibility?

Will the supplier arrange the connection of the system and correspondence with the electricity provider or is this my responsibility?

To get your system connected to the network, you need to apply for a new connection. As technical information is required, it’s a good idea to have your supplier to apply for you but you can also apply directly (some retailers will require this)
Your solar retailer will usually arrange the connection of your solar system to the network on your behalf, including preparing and submitting all relevant documentation required from the electricity retailer and/or distributor for meter installation and connection to the network. Most distribution companies require pre-approval to connect to their network. This should be done prior to installation as the approval process can take some time. (Ref, CEC)
You may also need to have your electricity meter replaced or reconfigured.  
See below for steps in each state: