How to disable content pagination?

I want to totally disable this functionality from WordPress because I’m implementing my own version of this with Javascript.

When I try to grab all the content in a post via the get_the_content() or the_content() it gives me only the first page, since the content has the page breaks. When I use $post->the_content I get the full post but it’s not formatted with HTML tags. I don’t want to have to add those myself programatically.

So I either need to get all the content already formatted – the way to do this is unknown to me at the moment
or disable wp_page_links() so it doesn’t paginate my posts.

EDIT – Now that 4.4 is out, you should use the content_pagination filter. See birgire’s answer below.

You can add formatting to raw post content by applying the content filters directly to $post->post_content:

echo apply_filters( 'the_content', $post->post_content );

This will bypass pagination by not using the get_the_content function, which is what the_content uses internally to retrieve the current page’s content for multipage posts.

You can prevent wp_link_pages from outputting anything by applying a filter to its output before the function is called and using the __return_empty_string helper function:

add_filter( 'wp_link_pages', '__return_empty_string' );