This paper presents the introduction of context dependent Hidden Markov Models for cursive, unconstrained handwriting recognition with large vocabularies. Since context dependent models were successfully introduced to speech recognition, it seems obvious that the use of trigraphs could also lead to improved on-line handwriting recognition systems. In analogy to triphones in speech recognition, trigraphs are context dependent sub-word units representing a single written character in its left and right context.The tests were conducted on a writer dependent system with three different writers and two different vocabulary sizes (1000 words and 30000 words). The results we obtained with the trigraph-based system compared to the monograph system are very encouraging: A mean relative error reduction of 46% for the 1000 word handwriting recognition system and a mean relative error reduction of 37% for the same system with the 30000 word vocabulary. We believe that this represents one of the first systematic investigations of the influence of context dependent models and parameter reduction methods for a difficult large vocabulary handwriting recognition task.