Anonymous Node Create
This project is not covered by Drupal’s security advisory policy.
The project is now moved to drupal.org and can be downloaded in this page.
The module allows anonymous users to create nodes. But 'anonymous' is questionable in this module. This module alters the node form for anonymous users by adding two field groups at the end before the save button.
The first field group has fields that allow users to create a new account. This new account is then the author of the new node created.
The second field group has fields that allow users to login to their account. The newly created node is then added to logged in user.
So in short, while the users can create nodes as anonymous users, the created node is then owned by a valid drupal user.
Additionally, if you install logintoboggan module and configure it to set password during registration, this module provides an field to set password during node creation.