Automatically create new window on second monitor?

Say a sovereign application has detected that a user has multiple monitors.

If the user initiates the creation of an additional window -- a window that needs to be large -- what are the advantages and disadvantages to creating the new window maximized on a different monitor than the initiating window?

An obvious benefit is that the content of both windows continues to be visible.

Are there concerns about whether the user notices the new window appearing in her peripheral vision?

Do platform-specific UI style guides recommend for or against this? Are there platform-specific concerns, such as the behavior on Mac with multiple desktops on multiple monitors?