my harddisk is not big enough

gerhard212 wrote:

my harddisk is not big enough, can I download Big Sur onto an external storage?

If the 12 GB download pack is stored externally, I should have enough space on the internal storage.

How to free up storage space on your Mac - Apple Support

https://support.apple.com/en-us/HT206996

Big Sur states that you will need 35.5 GB of free storage when upgrading from High Sierra or newer, and 44.5 GB when upgrading from an older versions.

Externally you can create a bootable USB installer as a work a round:

How to create a bootable installer for macOS - Apple Support

Hi,

I think you can't install Big Sur from external drive on internal drive.