After myocardial infarction (MI), a significant portion of heart muscle is replaced with scar tissue, progressively leading to heart failure. Human pluripotent stem cell-derived cardiomyocytes (hPSC-CM) offer a promising option for improving cardiac function after MI. However, hPSC-CM transplantation can lead to engraftment arrhythmia (EA). EA is a transient phenomenon arising shortly after transplantation then spontaneously resolving after a few weeks. The underlying mechanism of EA is unknown. We hypothesize that EA may be explained partially by time-varying, spatially heterogeneous, graft-host electrical coupling. Here, we created computational slice models derived from histological images that reflect different configuration of grafts in the infarcted ventricle. We ran simulations with varying degrees of connection imposed upon the graft-host perimeter to assess how heterogeneous electrical coupling affected EA with non-conductive scar, slow-conducting scar and scar replaced by host myocardium. We also quantified the effect of variation in intrinsic graft conductivity. Susceptibility to EA initially increased and subsequently decreased with increasing graft-host coupling, suggesting the waxing and waning of EA is regulated by progressive increases in graft-host coupling. Different spatial distributions of graft, host and scar yielded markedly different susceptibility curves. Computationally replacing non-conductive scar with host myocardium or slow-conducting scar, and increasing intrinsic graft conductivity both demonstrated potential means to blunt EA vulnerability. These data show how graft location, especially relative to scar, along with its dynamic electrical coupling to host, can influence EA burden; moreover, they offer a rational base for further studies aimed to define the optimal delivery of hPSC-CM injection. KEY POINTS: Human pluripotent stem cell-derived cardiomyocytes (hPSC-CM) hold great cardiac regenerative potential but can also cause engraftment arrhythmias (EA). Spatiotemporal evolution in the pattern of electrical coupling between injected hPSC-CMs and surrounding host myocardium may explain the dynamics of EA observed in large animal models. We conducted simulations in histology-derived 2D slice computational models to assess the effects of heterogeneous graft-host electrical coupling on EA propensity, with or without scar tissue. Our findings suggest spatiotemporally heterogeneous graft-host coupling can create an electrophysiological milieu that favours graft-initiated host excitation, a surrogate metric of EA susceptibility. Removing scar from our models reduced but did not abolish the propensity for this phenomenon. Conversely, reduced intra-graft electrical connectedness increased the incidence of graft-initiated host excitation. The computational framework created for this study can be used to generate new hypotheses, targeted delivery of hPSC-CMs.