When does 木 as a character component get detached legs? Is there any discernible rule concerning whether 木 as a component of a character has attached legs (as in 李) or has detached legs (as in 新)? Worse, this seems to vary from country to country.
To start off,「木」is not supposed to have detached legs and end up looking like「朩」. In one of the most stringent glyph standards, Kangxi Dictionary style Ming (Serif), if the Shuowen small seal shape contains「木」, then it does not have detached legs.

This is for glyph shape fidelity reasons, and conversely, if it has detached legs, you can be certain that, at the very least, the Kangxi Dictionary didn't think that it came from the component「木」.

Of course, this sometimes doesn't turn out correctly, as with ancient characters which were no longer used, such as「亲」and characters which use it as a component.


For reference,「亲」(hazel tree) is a variation of「」, and is constructed from semantic「木」and phonetic「辛」. This word is now written as「榛」.
西周金中伯壺集成9668篆木部說文解字臺標楷　臺標隸定　

Detached legs on「木」are strictly an invention from calligraphy, and overwhelmingly occur on the bottom of characters:

Thus, all character shapes directly affected by calligraphy, including those set by government standards, will have a chance of containing「木」appearing with detached legs. This is purely a shape phenomenon - it has nothing to do with the language.

Characters which are affected by calligraphy are:
(1) The Taiwanese MoE standard, which actively prescribes writing「木」on the bottom as「朩」, and this effect has bled into their print fonts.

(2) PRC's regularised cursive shapes

But I guess it is arguable whether regularised cursive is appropriate for any kind of character shape analysis.