Horizontal gene transfer (HGT) is a prevalent and a highly important phenomenon in microbial species evolution. One of the important challenges in HGT research is to better understand the factors that determine the tendency of genes to be successfully transferred and retained in evolution (i.e., transferability). It was previously observed that transferability of genes depends on the cellular process in which they are involved where genes involved in transcription or translation are less likely to be transferred than metabolic genes. It was further shown that gene connectivity in the protein-protein interaction network affects HGT. These two factors were shown to be correlated, and their influence on HGT is collectively termed the "Complexity Hypothesis". In this study, we used a stochastic mapping method utilizing advanced likelihood-based evolutionary models to quantify gene family acquisition events by HGT. We applied our methodology to an extensive across-species genome-wide dataset that enabled us to estimate the overall extent of transfer events in evolution and to study the trends and barriers to gene transferability. Focusing on the biological function and the connectivity of genes, we obtained novel insights regarding the "complexity hypothesis." Specifically, we aimed to disentangle the relationships between protein connectivity, cellular function, and transferability and to quantify the relative contribution of each of these factors in determining transferability. We show that the biological function of a gene family is an insignificant factor in the determination of transferability when proteins with similar levels of connectivity are compared. In contrast, we found that connectivity is an important and a statistically significant factor in determining transferability when proteins with a similar function are compared.