Are scholarships offered to out of state students if they want to apply to schools such as UC Berkeley and UCLA?

Answered

Yes, you can get regents and chancellor if you are out of state.

For those specific examples yes—named scholarships like Regents or Chancellors are usually offered to both in- and out-of-state students at schools like the UCs.

However, in general, merit aid at state schools will be offered much more to in-state than out-of-state students. If you can't get one of those big scholarships at a school like Berkeley or UCLA (or say the Robertson Scholarship for UNC, as another example), you're unlikely to get any other kind of aid from them.