A narration where its sanad has no person omitted or missing up to its stated end such as the Prophet ﷺ.
Allamah Nawawi states in Taqrib1 states:
[Muttasil] is also called Mawsul. It is a sanad which is connected2 [without the omission of a person in between] be it marfu3 or mawquf4 .
The term muttasil will be qualified with a name, if the sanad is only connected up to a specific narrator such as if the sanad terminates upon Zuhri, it will be said Muttasil ila Zuhri rather than simply saying Muttasil. Muttasil when said simply generally indicates that it is marfu'.
Muttasil is not compatible with munqati'5 and mu'dhal6 .
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Further reading
Fath al-Mugith li Sakhawi pp.185-6 v.1
Tadrib al-Rawi li Suyuti ma'a Taqrib al-Nawawi p. 94 v. 1