Three ways to split
Every page makes one PDF per page. Page ranges takes what you type, like 1-3, 4-6, 7-, and makes one PDF per range (7- runs to the end). Pages I pick lets you click the pages you want and saves them as one PDF. More than one file comes back as a single ZIP.
Nothing is lost
Pages are copied as they are, so text stays selectable and pictures keep their quality. The original file is not changed.
Questions
Is my PDF uploaded?
No. It is split in this page, on your device. Nothing is sent anywhere.
Can I split a password-protected PDF?
Not if it needs a password to open, or is encrypted against changes. Remove the protection in the program that made it, then split it here.