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Archdeacon, in his seminal paper $[1]$, defined the concept of Heffter arrayin order to provide explicit constructions of $\mathbb{Z}_{v}$-regularbiembeddings of complete graphs $K_v$ into orientable surfaces.  In this paper, we first introduce the quasi-Heffter arrays as ageneralization of the concept of Heffer array and we show that, in thiscontext, we can define a $2$-colorable embedding of Archdeacon type of thecomplete multipartite graph $K_{\frac{v}{t}\times t}$ into an orientablesurface. Then, our main goal is to study the full automorphism groups of theseembeddings: here we are able to prove, using a probabilistic approach, that,almost always, this group is exactly $\mathbb{Z}_{v}$.  As an application of this result, given a positive integer $t\not\equiv0\pmod{4}$, we prove that there are, for infinitely many pairs of $v$ and $k$,at least $(1-o(1)) \frac{(\frac{v-t}{2})!}{\phi(v)} $ non-isomorphicbiembeddings of $K_{\frac{v}{t}\times t}$ whose face lengths are multiples of$k$. Here $\phi(\cdot)$ denotes the Euler's totient function. Moreover, in case$t=1$ and $v$ is a prime, almost all these embeddings define faces that are allof the same length $kv$, i.e. we have a more than exponential number ofnon-isomorphic $kv$-gonal biembeddings of $K_{v}$.

Biembeddings of Archdeacon type: their full automorphism group and their number