The query has some assumptions that do not hold for Sanskrit. The Sanskrit grammars deal with phonemes but not with written letters. Joint phonemes will be the correct phrase. There is nothing on ligatures in Sanskrit grammar that necessarily belong to scripts. The concept of ligature grew in the first millennium.
saṃyoga is the accepted term for consonantal conjunct. If we go by the akṣara concept every akṣara is a combination of consonant/s and a vowel, hence joint too.
Sanskrit orthography goes by its own law of akara. This has been touched in some of the nineteenth century grammars of Sanskrit. In writing, the final a is understood but not the other vowels. Hence kapāla = कपाल. There is one ligature here but it is not recognized in Sanskrit grammar as saṃyoga. In the क्ता of vaktā one gets a more complex ligature.  The –kt- is a saṃyoga.
I hope the position is clear.

From: Harsha Dehejia <harshadehejia@HOTMAIL.COM>
Sent: Saturday, 3 March 2012 6:31 PM
Subject: [INDOLOGY] Joint Letters

I am researching the tradition of joining two letters.
1. In the bhashas it is called jodakshara. What is the Sanskrit word for this?
2. Is this in any way related to joining two images as in Ardhanari or Harihara?
3. What is the semantic impact of joining two letters or images?
Kind regards.
Prof. Harsha V. Dehejia
Ottawa, ON., Canada.