Transposons are discrete segments of DNA that have the distinctive ability to move and replicate within genomes across the tree of life. 'Cut and paste' DNA transposition involves excision from a donor locus and reintegration into a new locus in the genome. We studied molecular events following the excision steps of two eukaryotic DNA transposons, Sleeping Beauty (SB) and piggyBac (PB) that are widely used for genome manipulation in vertebrate species. SB originates from fish and PB from insects; thus, by introducing these transposons to human cells we aimed to monitor the process of establishing a transposon-host relationship in a naïve cellular environment. Similarly to retroviruses, neither SB nor PB is capable of self-avoidance because a significant portion of the excised transposons integrated back into its own genome in a suicidal process called autointegration. Barrier-to-autointegration factor (BANF1), a cellular co-factor of certain retroviruses, inhibited transposon autointegration, and was detected in higher-order protein complexes containing the SB transposase. Increasing size sensitized transposition for autointegration, consistent with elevated vulnerability of larger transposons. Both SB and PB were affected similarly by the size of the transposon in three different assays: excision, autointegration and productive transposition. Prior to reintegration, SB is completely separated from the donor molecule and followed an unbiased autointegration pattern, not associated with local hopping. Self-disruptive autointegration occurred at similar frequency for both transposons, while aberrant, pseudo-transposition events were more frequently observed for PB.