We provide a process for making a fuel or lubricant component, comprising: performing alkylation and oligomerization by contacting a stream comprising one or more olefins and one or more isoparaffins, wherein a molar ratio of the one or more olefins to the one or more isoparaffins in the stream is at least 0.8, an acidic chloroaluminate ionic liquid catalyst, and a halohalide; and recovering the fuel or lubricant component having a Bromine Number of less than 4. We provide a process comprising performing concurrent alkylation and oligomerization. We also provide a process for making a lubricant component having a kinematic viscosity at 100.degree. C. of at least 6.9 mm.sup.2/s, a VI of at least 134, a cloud point less than or equal to -28.degree. C., and a Bromine Number of less than or equal to 6.1.