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Y₂CuTiO₆ contains edge-shared triangular planes where the vertices are occupied by magnetic Cu and nonmagnetic Ti atoms in equal proportion. In spite of the large dilution of the triangular magnetic lattice, the magnetic susceptibility shows a large, AF θ_CW of about 240 K without any sign of ordering down to 1.8 K. No bifurcation is observed in the ZFC/FC magnetisation data in a low field of 50 Oe, down to 0.5 K. Likewise, the heat capacity shows no anomalies and the magnetic contribution has a power law behaviour at low-temperatures. Our muSR measurements down to 50 mK also do not show any signs of ordering. These observations are typical of potential quantum spin liquid systems. In the present case, however, the magnetic heat capacity C_m depends on the magnetic field H. We observed that the data could be scaled such that H^γC_m/T vs T/H follows a universal curve with γ = 0.6. Such a scaling behaviour has been suggested in systems with random singlet formation. The randomness of exchange coupling in Y₂CuTiO₆ might be due to the random occupation of Cu and Ti on the vertices of triangles. It is nevertheless surprising that in spite of the large (50%) depletion of the lattice, no spin freezing is observed.