Single copy genes, universally distributed across the three domains of life and encoding mostly ancient parts of the translation machinery, are thought to be only rarely subjected to horizontal gene transfer (HGT). Indeed it has been proposed to have occurred in only a few genes and implies a rare, probably not advantageous event in which an ortholog displaces the original gene and has to function in a foreign context (orthologous gene displacement, OGD). Here, we have utilised an automatic method to identify HGT based on a conservative statistical approach capable of robustly assigning both donors and acceptors. Applied to 40 universally single copy genes we found that as many as 68 HGTs (implying OGDs) have occurred in these genes with a rate of 1.7 per family since the last universal common ancestor (LUCA). We examined a number of factors that have been claimed to be fundamental to HGT in general and tested their validity in the subset of universally distributed single copy genes. We found that differing functional constraints impact rates of OGD and the more evolutionarily distant the donor and acceptor, the less likely an OGD is to occur. Furthermore, species with larger genomes are more likely to be subjected to OGD. Most importantly, regardless of the trends above, the number of OGDs increases linearly with time, indicating a neutral, constant rate. This suggests that levels of HGT above this rate may be indicative of positively selected transfers that may allow niche adaptation or bestow other benefits to the recipient organism.