Abstract Compact power splitters are essential components in integrated optics. While 1 × 2 power splitters with uniform splitting are widely used, a 1 × N splitter with arbitrary number N of ports and arbitrary splitting ratio is yet to be demonstrated. In this work we address this problem. We fabricate and characterise 1 × N integrated power splitters that provide fully arbitrary splitting ratios. The core of our design is represented by an array of N non-equally spaced waveguides fabricated on a silicon nitride-on-insulator wafer. Any arbitrary 1 × N splitting ratio can be achieved by properly setting the array length and the dimension of the (N–1) nano-gaps between the adjacent waveguides. Most importantly, at variance with state-of-the-art solutions, our devices can be designed for arbitrary splitting of higher-order modes. In this manuscript we provide the first experimental demonstration of 1 × N arbitrary splitting ratio for both the fundamental modes (TE00 and TM00) and the TE01 mode, here up to N = 5 ports. With a footprint of 20 μm²/port, a bandwidth up to 70 nm and an excess losses <0.2 dB, our devices set a new benchmark for optical power splitters in both standard single-mode photonics as well as in the emerging integrated multimode photonics technology, and may therefore boost key photonic applications, from optimal power distribution and equalization up to signal processing operations.