Seems like my description was incorrect. I meant that there are two ways to deal with text: line-wise and fragment-wise.
In most other text editors, if you copy a line, and then paste it, it gets pasted into the cursor position regardless whether you copied a line or a fragment (fragment-wise). In Vim, lines yanked with 'yy' disregard the cursor column and get pasted into a line above or below, while fragments yanked with 'y' (e.g. '0y$'), take into account the column.
I like how in Vim you can do line-wise editing, but I just miss an easy way to paste text to the position starting with the current column regardless of the way I yanked it.
PS Thanks everyone for replies!
Mapping the leader to , and it's even nicer. then all you need to do is ,y and you get the line in fragment mode.
nnoremap <leader>y 0y$
or if you want just first non whitespace char you could do an uppercase y for the leader command. swap the upper and lower to make it how you want. seems like this would be a more useful command to have:
nnoremap <leader>Y ^y$
edit: saw that you found a workaround by pasting in insert mode. ctrl-r" any other ways to paste in insert mode?
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If you want to yank a line character-wise, you would do something like ^y$. I have Y mapped to y$ for this sort of thing.
You cannot yank a substring of a line line-wise. That doesn't really make sense. I typically open a new line with o and then paste in insert mode with <C-r>". So o<C-r>".