Recent discoveries have led to renewed hope for making major inroads into HIV epidemics, including pre-exposure prophylaxis, early treatment as prevention, and more sensitive HIV tests. The relative cost-effectiveness of these interventions will depend on the contexts in which transmission events are currently occurring, a topic currently subject to strong debate. In this work, my colleagues and I sought to estimate the proportions of transmissions occurring in main vs. casual partnerships, and by the sexual role, infection stage, and testing and treatment history of the infected partner, for men who have sex with men (MSM) in the US and Peru. To represent observed sexual networks, we use a pair of linked exponential random graph models (ERGMs), one cross-sectional and one temporal, each parametrized by multiple large-scale MSM surveys. This approach reveals a number of novel statistical and computational issues for ERGMs, which we discuss. We interpret our results in the context of existing estimates, and their implications for prevention strategies.