It is so important to provide a complete description from the beginning.

This solution copies the first file, and pastes it starting at A1 of the master.
It copies the second file, then pastes it starting in column A, in the row after the end of the data from the first file.
And so on.

How is that copying "on the master across the columns"? It is pasting downwards. What does it mean to copy "(without the header) below the columns"? A column is cells of data; there is no such thing as below a column.

I suggest you build a master by hand by copying and pasting just two files, and then attach all three files so I can see exactly what you want the result to look like.