The alkylation reaction of isobutane with trans-2-butene has been carried out on a series of steam-dealuminated Y zeolites with unit cell sizes ranging from 2.450 to 2.426 nm. A fixed-bed reactor connected to an automatized multiloop sampling system allowed us to make differential product analysis from very short (1 min or less) to longer times on stream. A maximum in the initial 2-butene conversion was found on samples with unit cell sizes between 2.435 and 2.450 nm. However, the TMP/DMH ratio, i.e., the alkylation-to-oligomerization ratio, continuously increased with zeolite unit cell size. The concentration of reactants in the pores, the strength distribution of Bronsted acid sites, and the extent of hydrogen transfer reactions, which in turn depend on the framework Si/Al ratio of a given zeolite, were seen to affect activity and product distribution of the catalysts. Finally, the influence of these factors on the aging characteristics of the samples was also discussed.