A method of preparing an immobilized library of tagged DNA fragments comprising: (a) providing a solid support having a plurality of transposome complexes immobilized thereon, wherein said transposome complexes each comprise: a transposase non-covalently bound to a first polynucleotide of a double-stranded nucleic acid comprising the first and a second polynucleotide, wherein said first polynucleotide is immobilized to said solid support, and wherein said first polynucleotide comprises (i) a 3' portion comprising a transposon end sequence, and (ii) a first tag comprising a first tag domain; and wherein said second polynucleotide comprises a region complementary to said transposon end sequence; and wherein the transposome complexes are homodimers, the homodimers comprising a first plurality of homodimers comprising a first tag of a first sequence and a second plurality of homodimers comprising a first tag of a second sequence; (b) applying a target double-stranded DNA to the solid support under conditions whereby the target DNA is fragmented by the transposome complexes, and the 3' transposon end sequence of the first polynucleotide is transferred to a 5' end of at least one strand of the fragments; thereby producing an immobilized library of double-stranded fragments wherein at least one strand is 5'-tagged with the first tag of the first sequence and at least one strand is 5'-tagged with the first tag of the second sequence. (a) providing a solid support having a plurality of transposome complexes immobilized thereon, wherein said transposome complexes each comprise: a transposase non-covalently bound to a first polynucleotide of a double-stranded nucleic acid comprising the first and a second polynucleotide, wherein said first polynucleotide is immobilized to said solid support, and wherein said first polynucleotide comprises (i) a 3' portion comprising a transposon end sequence, and (ii) a first tag comprising a first tag domain; and wherein said second polynucleotide comprises a region complementary to said transposon end sequence; and wherein the transposome complexes are homodimers, the homodimers comprising a first plurality of homodimers comprising a first tag of a first sequence and a second plurality of homodimers comprising a first tag of a second sequence; a transposase non-covalently bound to a first polynucleotide of a double-stranded nucleic acid comprising the first and a second polynucleotide, wherein said first polynucleotide is immobilized to said solid support, and wherein said first polynucleotide comprises (i) a 3' portion comprising a transposon end sequence, and (ii) a first tag comprising a first tag domain; (i) a 3' portion comprising a transposon end sequence, and (ii) a first tag comprising a first tag domain; and wherein said second polynucleotide comprises a region complementary to said transposon end sequence; and wherein the transposome complexes are homodimers, the homodimers comprising a first plurality of homodimers comprising a first tag of a first sequence and a second plurality of homodimers comprising a first tag of a second sequence; (b) applying a target double-stranded DNA to the solid support under conditions whereby the target DNA is fragmented by the transposome complexes, and the 3' transposon end sequence of the first polynucleotide is transferred to a 5' end of at least one strand of the fragments; thereby producing an immobilized library of double-stranded fragments wherein at least one strand is 5'-tagged with the first tag of the first sequence and at least one strand is 5'-tagged with the first tag of the second sequence.