The jailbreak property that, if the user turns the device off and back on, the device will start up completely, and the kernel will be patched without the help of a computer - in other words, it will be jailbroken after each reboot - comes under which type?

An untethered jailbreak.

Explanation:

Jailbreaking is the process of installing a modified set of kernel patches that in turn enables users to run third-party applications not endorsed by the Operating System vendor. It is the sytem of bypassing user bridges as set by Apple, such as modifying the OS, having admin privileges, and ability to install unofficially applications that are approved by "side loading."

There are different types of jailbreak. An untethered jailbreak uses mechanisms that are extremely strong enough to allow the user to turn their device off and on at will, with the device starting up completely, & the kernel will be patched but without the help of a computer which means it will be jailbroken even after each reboot.