Does the <basefont> tag exist and what is its function?

No, the <basefont> tag does not exist in the current HTML5 standard.

Previously, in HTML4, there was a <basefont> tag. Its function was to set basic font parameters (size, color, font) for the entire document.

Example of usage in HTML4:

<basefont size="3" color="blue" face="Arial">

This tag was deprecated and is not recommended for use. The modern approach for styling fonts is to use CSS.