We study the boundary behaviour of the solutions of (E) \Delta_p u+|\nabla u|^q=0 in a domain \Omega \subset \mathbb R^N, when N\geq p> q>p-1. We first recall the results obtained in the case p=2: boundary trace, boundary isolated or removable singularities. In the case p\neq 2, we show the existence of a critical exponent q_* < p such that if p-1 < q < q_* there exist positive solutions of (E) with an isolated singularity on \partial \Omega and that these solutions belong to two types of singular solutions. If q_*\leq q < p no such solution exists and actually any boundary isolated singularity of a positive solution of (E) is removable. We prove that all the singular solutions are classified according the two types of singular solutions that we have constructed. An extension to a geometric framework is also presented as a consequence of a general estimate. The case p=2 is a joint paper with T. Nguyen Phuoc. The case p\neq 2 corresponds to a work in progress with M.F. Bidaut-Vèron and M.