Determining the exact country with the most pets per capita can be challenging due to variations in data collection methods and availability. However, some countries are often recognized for their high pet ownership rates. As of my knowledge cutoff in September 2021, the following countries are often considered to have high pet ownership per capita:

1. United States: The United States has a significant pet population, with approximately 67% of households owning a pet according to the American Pet Products Association (APPA).
2. Brazil: Brazil has a strong culture of pet ownership, and it is estimated that around 60% of households have pets.
3. Argentina: Similar to Brazil, Argentina has a high pet ownership rate, with around 60% of households having pets.
4. Mexico: Mexico has a considerable number of pet owners, and it is estimated that around 70% of households have pets.
5. Russia: Russia also has a high pet ownership rate, with dogs being particularly popular. The exact percentage of pet-owning households is not readily available.

It's important to note that the pet ownership rates and per capita data may have changed since my knowledge cutoff, and different sources may provide slightly different rankings. Additionally, factors such as cultural norms, economic conditions, and population density can influence pet ownership rates in different countries.