What is the correct auxiliary in a sentence like this:
In the last years the number of some-things is/has grown.
It depends on what you want to denote. I will follow that you really want to denote "the number of some-things" and the available options you gave. The correct answer would be (as John Lawler said):
In the last years, the number of some-things has grown.
This is because the event of the number growing is relevant to your (supposed) focus on the present.
Here are few other examples for different tenses:
Simple past (Event happened in the past):
In the last years, fifteen apple trees were grown.
Present perfect (Past event with present consequences):
In the last years, the number of apple trees has grown (by four percent).
I suspect this would also be acceptable if you want to focus on the present situation of the apple trees:
In the last years, fifteen apple trees have been grown.
Present continuous perfect (Event started in the past and is still happnening):
In the last years, the number of apple trees has been growing.
In the last years, fifteen apple trees have been growing.
Past perfect (Past event with later past consequences):
In 2000, the number of apple trees had grown since 1990.